- Generalized quotient rings,
*Proc. Amer. Math. Soc.*,**82**(1965), 795-799. - Direct sums of countable groups and related concepts,
*Journal of Algebra*,**2**(1965), 443-450. (with J. M. Irwin) - Primary abelian groups as modules over their endomorphism
rings,
*Math. Zeit.*,**89**(1965), 77-81. (with E. A. Walker) - Countable direct sums of torsion complete groups,
*Proc. Amer. Math. Soc.*,**17**(1966), 763-767. (with J. M. Irwin and E. A. Walker) - On a certain purification problem for primary abelian groups,
*Bull. Soc. Math. France*,**94**(1966), 207-210. (with C. L. Walker) - Cotorsion free, an example of relative injectivity,
*Math. Zeit.*,**102**(1967), 115-117. (with E. A. Walker) - Maximal subgroups of infinite symmetric groups,
*Canad. Math. Bull.*,**10**(1967), 375-381. - A class of rank-2 torsion-free groups,
*Studies on abelian groups*, Dunod, Paris 1968, 327-334. - Projective classes of abelian groups,
*ibid*, 335-344. (with C. Walker and E. Walker) - Thin abelian
*p*-groups,*Pac. J. Math.*,**27**(1968), 599-606. - Extending Ulm's theorem without group theory,
*Proc. Amer. Math. Soc.*,**21**(1969), 194-196. (with E. A. Walker) - Extensions of
*p*-bounded groups,*Archiv der Math.*,**21**(1970), 449-454. - Modules over PID's that are injective over their endomorphism
rings,
*Proc. Park City Utah Ring Theory Conference*, (1972), 363-372. (with E. A. Walker) - The constructive theory of countable abelian
*p*-groups,*Pac. J. Math.*,**45**(1973), 621-637. - Constructive aspects of Noetherian rings,
*Proc. Amer. Math. Soc.*,**44**(1974), 436-441. - The constructive Jordan curve theorem,
*Rocky Mtn. J. Math.*,**5**(1975), 225-236. (with G. Berg, W. Julian and R. Mines) - The constructive theory of KT-modules,
*Pac. J. Math.*,**61**(1975), 263-274. - Detachable
*p*-groups and quasi-injectivity,*Acta Math. Acad. Sci. Hung.*,**27**(1976), 71-73. - A constructive modification of Vietoris homology,
*Fund. Math.*,**XCI**(1976), 241-250. - Homological dimension of abelian groups over their endomorphism rings,
*Proc. Amer. Math. Soc.*,**54**(1976), 65-68. (with E. A. Walker) - Constructive dimension theory,
*Compositio Math.*,**33**(1976), 1-17. (with G. Berg, H. Cheng and R. Mines) - The constructive equivalence of covering and inductive dimensions,
*Gen. Top. and its Appl.*,**7**(1977), 99-108. (with G. Berg, W. Julian and R. Mines) - Computing heights in Tor,
*Houston J. Math.*,**3**(1977), 267-270. - Ext in pre-abelian categories,
*Pac. J. Math.*,**71**(1977), 521-535. (with E. A. Walker) - Finite direct sums of cyclic valuated
*p*-groups,*Pac. J. Math.*,**69**(1977), 97-104. (with R. Hunter and E. A. Walker) - Simply presented valuated abelian
*p*-groups,*Journal of Algebra*,**49**(1977), 125-133. (with R. Hunter and E. A. Walker) - A guide to valuated groups,
*Abelian group theory*, Lecture Notes in Mathematics,**616**(1977), Springer-Verlag, 73-86. - Warfield modules,
*ibid*, 87-123. (with R. Hunter and E. A. Walker) - Existence theorems for Warfield groups,
*Trans. Amer. Math. Soc.*,**235**(1978), 345-362. (with R. Hunter and E. A. Walker) - Algebraic numbers, a constructive development,
*Pac. J. Math.*,**74**(1978), 91-102. (with W. Julian and R. Mines) - Valuated groups,
*Journal of Algebra*,**56**(1979), 145-167. (with E. A. Walker) - Global Azumaya theorems in additive categories,
*J. Pure Appl. Alg.*,**16}**(1980), 223-242. (with D. Arnold and R. Hunter) - Cyclic Ext,
*Rocky Mtn. J. Math.*,**11**(1981), 611-615. (with E. A. Walker) - Global Warfield groups,
*Trans. Amer. Math. Soc.*,**266**(1981), 555-572. (with R. Hunter) - Compactly generated Banach spaces,
*Archiv der Mat.*,**36**(1981), 239-243. (with D. S. Bridges, A. Calder, W. Julian and R. Mines) - Epsilon-covering dimension,
*Pac. J. Math.*,**95**(1981), 257-262. (with W. Julian, R. Mines and A. Calder) - Mixed local groups,
*Abelian group theory*, Springer Lecture Notes**874**(1981), 374-404. - Seidenberg's condition P,
*Constructive mathematics*, Springer Lecture Notes**873**(1981), 1-11. - Dedekind domains,
*ibid*, 16-30. (with R. Mines) - Locating metric complements in Euclidean spaces,
*ibid*, 241-249. (with D. S. Bridges, A. Calder, W. Julian and R. Mines) - Bounded linear mappings of finite rank,
*J. Fcnl. Analysis*,**43**(1981), 143-148. (with D. S. Bridges, A. Calder, W. Julian and R. Mines) - Separability and factoring polynomials,
*Rocky Mtn. Math. J.*,**12**(1982), 43-54. (with R. Mines) - Meaning and information in constructive mathematics,
*Amer. Math. Monthly*,**89**(1982), 385-388. - Finite-dimensional algebras over discrete fields,
*Proc. Brouwer Centenary Symp.*, North-Holland 1982, 397-411. - Picard's theorem,
*Trans. Amer. Math. Soc.*,**269**(1982), 513-520. (with D. S. Bridges, A. Calder, W. Julian and R. Mines) - Alexander duality,
*Pac. J. Math.*,**106**(1983), 115-127. (with W. Julian and R. Mines) - Church's thesis without tears,
*J. Symbolic Logic*,**48**(1983), 797-803. - Group algebras of abelian groups,
*Rend. Sem. Mat. Padova*,**69**(1983), 41-50. (with D. Beers and E. A. Walker) - Mixed groups,
*Abelian group theory*, Springer Lecture Notes**1006**(1983), 445-470. - Nice subgroups of mixed local groups,
*Comm. in Alg.*,**11**(1983), 1629-1642. - An extension of the theory of completely decomposable torsion-free
abelian groups,
*Trans. Amer. Math. Soc.*,**279**(1983), 175-185. - A uniformly continuous function on [0,1] that is everywhere different
from its infimum,
*Pac. J. Math.*,**111**(1984), 333-340. (with W. Julian) - Butler groups, valuated vector spaces, and duality,
*Rend. Sem. Mat. Padova*,**72**(1984), 1-7. - Valuation theory: a constructive view,
*J. Number Theory*,**19**(1984), 40-62. (with R. Mines) - Subgroups of bounded abelian groups,
*Abelian groups and modules*, CISM Lectures**287**(1984), Udine, 17-36. (with R. Hunter and E. A. Walker) - Ulm's theorem for simply presented valuated
*p*-groups,*Abelian group theory*, Oberwolfach conference 1985, Gordon and Breach, London 1986, 33-64. (with R. Hunter and E. A. Walker) - Computing valuated trees,
*ibid*, 65-88. (with D. Beers, R. Hunter and E. A. Walker) - Archimedean valuations,
*J. London Math. Soc.*,**34**(1986), 403-410. (with R. Mines) - The intermediate value theorem: preimages of compact sets under
uniformly continuous functions,
*Rocky Mtn. J. Math.*,**18**(1988), 25-36. (with W. Julian and R. Mines) - Subgroups of finite direct sums of valuated cyclic groups,
*Journal of Algebra*,**114**(1988), 1-15. (with D. Arnold) - Computers, trees, and abelian groups,
*Computers and Math. with Appl.*,**15**(1988), 333-336. - Nontrivial uses of trivial rings,
*Proc. Amer. Math. Soc.*,**103**(1988), 1012-1014. - Separable extensions and diagonalizability,
*Amer. Math. Monthly*,**97**(1990), 395-398. - Intuitionism as generalization,
*Philosophia Mathematica*,**5**(1990), 124-128. - Polynomials and linear transformations,
*Linear Algebra and its Appls.*,**131**(1990), 131-137. - The constructive theory of torsion-free abelian groups,
*Communications in Algebra*,**18**(1990), 3913-3922. - A counterexample to a theorem of Argyros,
*Mat. Vesnik*,**42**(1990), 73-75. - General
*p*-valuations on abelian groups,*Communications in Algebra*,**19**(1991), 3075-3088. (with D. Arnold and C. Vinsonhaler) - A recursive counterexample to Debreu's theorem on the existence of a
utility function,
*Mathematical Social Sciences*,**21**(1991), 179-182. (with D. Bridges) - The constructive theory of countably generated Warfield modules,
*Abelian groups and noncommutative rings*, Contemporary Math.**130**(1992), AMS, 371-383. - Transcendental operators on a Banach space,
*Rocky Mtn. J. Math.*,**22**(1992), 697-704 - Extensions and fixed points of contractive maps,
*J. Math. Anal. and Appls.*,**165**(1992), 438-456. (with D. Bridges, W. Julian and R. Mines) - Field-independent representations of partially ordered sets,
*Forum Mathematicum*,**4**(1992), 348-357. (with D. M. Arnold) - A circular argument,
*The College Mathematics Journal*,**24**(1993), 160-162. - Well-quasi-ordered sets,
*Advances in Math.*,**97**(1993), 145-153. (with G. Stolzenberg) - Representations of finite posets and valuated groups,
*Journal of Algebra*,**155**(1993), 110-126. (with D. Arnold and C. Vinsonhaler) - Isomorphism of Butler groups at a prime,
*Contemp. Math.*,**171**(1994), 333-337. - Calculating maximum-entropy probability densities for belief functions,
*Int. J. Uncertainty, Fuzziness and Knowledge Based Systems*,**2**(1995), 377-389. (with A. Meyerowitz and E. A. Walker). - Intuitionistic abelian group theory,
*Abelian groups and modules*, Arnold and Rangaswamy eds., Marcel Dekker 1996, 67-72. - Interview with a constructive mathematician,
*Modern Logic*,**6**(1996), 247-271. - Sets, complements and boundaries,
*Indagationes Mathematicae*,**7**(1996), 425-445, (with D. Bridges and Wang Yuchuan). - Growing forests in abelian
*p*-groups,*Journal of Algebra*,**187**(1997), 289-294. - Flat dimension, constructivity, and the Hilbert syzygy theorem,
*New Zealand J. Math.*,**26**(1997), 263-273. - Filtered modules over discrete valuation domains,
*Journal of Algebra*,**199**(1998), 618-645, (with E. Walker). - The regular element property,
*Proc. Amer. Math. Soc.*,**126**(1998), 2123--2129. - Generalized real numbers in constructive mathematics,
*Indagationes Mathematicae*,**9**(1998), 595-606. - Simply presented tag modules,
*Communications in Algebra*,**27**(1999), 1629-1648. - Nontransitivity of locatedness for subspaces of a Banach space,
*Far East Journal of Mathematical Sciences*,**1**(1999), 175-179. - Existence proofs,
*American Mathematical Monthly*,**106**(1999), 303-308. - A constructive proof of Gleason's theorem,
*Journal of Functional Analysis*,**162**(1999), 287-312, (with Douglas Bridges). - Is 0.999... = 1?,
*Mathematics Magazine*,**72**(1999), 404-408. - Subgroups of
*p*^{5}-bounded groups, in*Abelian groups and modules*, Birkhäuser 1999, 55-73 (with Elbert Walker). - Linear independence without choice,
*Annals of Pure and Applied Logic*,**101**(2000), 95-102, (with Douglas Bridges and Peter Schuster). - Some group theoretic aspects of t-norms,
*Int. J. Uncertainty, Fuzziness, and Knowledge Based Systems*,**8**(2000), 1-6, (with Elbert Walker). - A weak countable choice principle,
*Proc. Amer. Math. Soc.*,**128**(2000), 2749-2752, (with Douglas Bridges and Peter Schuster). - Weakly integrally closed domains: minimum polynomials of matrices,
*Communications in Algebra*,**28**(2000), 4735-4748, (with James Brewer). - Smooth invariants and omega-graded modules over
*k*[*X*],*Commentationes Mathematicae Universitatis Carolinae*,**41**(2000), 445--448. - Gleason's theorem has a constructive proof,
*Journal of Philosophical Logic*,**29**(2000), 425-431. - Adjoints, absolute values, and polar decompositions,
*J. Operator Theory*,**44**(2000), 243-254, (with Douglas Bridges and Peter Schuster). - The fundamental theorem of algebra: a constructive development without choice,
*Pacific Journal of Mathematics*,**196**(2000), 213-230. - Adjoints and the image of the ball,
*Proc. Amer. Math. Soc.*,**129**(2001), 1189-1193. - Constructive mathematics without choice,
*Reuniting the antipodes---constructive and nonstandard views of the continuum*, Schuster et al. eds., Kluwer, Synthese Library**306**(2001), 199--205. - Pointwise differentiability,
*Reuniting the antipodes---constructive and nonstandard views of the continuum*, Schuster et al. eds., Kluwer, Synthese Library**306**(2001), 207--210. - Omniscience principles and functions of bounded variation,
*Mathematical Logic Quarterly*,**42**(2002), 111-116. - Computing limiting stationary distributions of small noisy networks,
*Journal of Applied Probability*,**39**(2002), 1-18 (with Katarzyna Winkowsa-Nowak). - Trace-class operators,
*Houston Journal of Mathematics*,**28**(2002), 565-583 (with Douglas S. Bridges and Peter Schuster). - Spreads and choice in constructive mathematics,
*Indagationes Mathematicae*,**13**(2002), 259-267. - Pre-abelian clan categories,
*Rocky Mountain J. Math.*,**32**(2002), 1605-1616. - The ascending tree condition: constructive algebra without countable choice,
*Communications in Algebra*,**31**(2003), No. 4, 1993-2002. - The polydisk Nullstellensatz,
*Proc. Amer. Math. Soc.*,**132**(2004), Number 7, 2133-2140, (with Douglas Bridges, Ray Mines, and Peter Schuster). - Constructive
aspects of Markov chains,
*Journal of Universal Computer Science*,**11**, (2005) 2046-2055 (electronic) - A division algorithm,
*Journal of Algebra and its Applications*,**4**(2005), Number 4, 441-449. - Enabling
conditions for interpolated rings,
*Proceedings of the Dagstuhl Seminar on Mathematics, Algorithms, and Proofs*(2006). - Pi-balanced torsion-free modules over a discrete valuation domain,
*J. Alg.*,**295**(2006), 269-288, (with David M. Arnold and K. M. Rangaswamy). - Did Euclid need the Euclidean algorithm to prove unique factorization?,
*Amer. Math. Monthly*,**113**(2006), 196-205, (with David Pengelley). - Van der Waerden's construction of a splitting field,
*Comm. Algebra*,**34**(2006), 2351-2356. - Near convexity, metric convexity and convexity,
*Rocky Mountain Journal of Mathematics*,**37**(2007), 1305-1314. - Almost locatedness in uniform spaces,
*Czechoslovak Math. J.*,**57**(2007), 1-12, (with Bridges, Ishihara, Mines, Schuster, and Vita). - Subrings of zero-dimensional rings,
*Multiplicative ideal theory in commutative rings*, Springer 2007, 73-88, (with Jim Brewer)

*Mathematics for the liberal arts student*, Brooks-Cole, Belmont, California (1967). (with C. Walker and R. Wisner). Second edition (1973).*College trigonometry*, Scott, Foresman, and Co., Chicago (1970). (with C. Walker and E. A. Walker)*Number theory, an introduction to algebra*, Brooks-Cole, Monterey, California, (1971).*Varieties of constructive mathematics*, London Math. Soc. Lecture Notes Series**97**, Cambridge 1987. (with D. S. Bridges)*A course in constructive algebra*, Springer-Verlag 1988. (with R. Mines and W. Ruitenburg)*Numbers and symmetry: an introduction to algebra*, CRC Press 1997. (with B. L. Johnston)*Mathematics for the liberal arts student*, Prentice-Hall (2000). (with C. Walker, R. Wisner, and J. Brewer)*Mathematics for liberal arts*, Kendall/Hunt (2002). (with C. Walker, R. Wisner, and J. Brewer)*Applied Algebra: Codes, Ciphers, and Discrete Algorithms*, Second Edition, CRC Press (2009). (with Darel W. Hardy and Carol L. Walker)

Last modified 5 December 2010