Fred Richman

Articles

• 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 p⁵-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)

Books

• 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)