The mathematical work of Morgan Ward
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References
- Morgan Ward, A generalization of recurrents, Bull. Amer. Math. Soc. 33 (1927), no. 4, 477–492. MR 1561403, DOI 10.1090/S0002-9904-1927-04410-X General arithmetic, Proc. Nat. Acad. Sci. U.S.A. 13 (1927), 748-749. Postulates for an abstract arithmetic, Proc. Nat. Acad. Sci. U.S.A. 14 (1928), 907-911.
- Morgan Ward, A Simplification of Certain Problems in Arithmetical Division, Amer. Math. Monthly 35 (1928), no. 1, 9–14. MR 1521339, DOI 10.2307/2298578
- Morgan Ward, On Certain Functional Relations, Amer. Math. Monthly 36 (1929), no. 8, 426–431. MR 1521822, DOI 10.2307/2299940 Certain expansions involving doubly infinite series, Ann. of Math. (2) 30 (1929), 578-582.
- Morgan Ward, A certain class of polynomials, Ann. of Math. (2) 31 (1930), no. 1, 43–51. MR 1502917, DOI 10.2307/1968138 A generalization of a familiar theorem concerning prime numbers, J. London Math. Soc. 5 (1930), 106-107. The reversion of a power series, Rend. Circ. Mat. Palermo 54 (1930), 42-46.
- Morgan Ward, Postulates for the inverse operations in a group, Trans. Amer. Math. Soc. 32 (1930), no. 3, 520–526. MR 1501550, DOI 10.1090/S0002-9947-1930-1501550-7
- Morgan Ward, The characteristic number of a sequence of integers satisfying a linear recursion relation, Trans. Amer. Math. Soc. 33 (1931), no. 1, 153–165. MR 1501582, DOI 10.1090/S0002-9947-1931-1501582-X
- Morgan Ward, The algebra of recurring series, Ann. of Math. (2) 32 (1931), no. 1, 1–9. MR 1502975, DOI 10.2307/1968408
- Morgan Ward, Some arithmetical properties of sequences satisfying a linear recursion relation, Ann. of Math. (2) 32 (1931), no. 4, 734–738. MR 1503026, DOI 10.2307/1968316
- Morgan Ward, The distribution of residues in a sequence satisfying a linear recursion relation, Trans. Amer. Math. Soc. 33 (1931), no. 1, 166–190. MR 1501583, DOI 10.1090/S0002-9947-1931-1501583-1
- Morgan Ward, Conditions for the solubility of the Diophantine equation $x^2-My^2=-1$, Trans. Amer. Math. Soc. 33 (1931), no. 3, 712–718. MR 1501611, DOI 10.1090/S0002-9947-1931-1501611-3
- Morgan Ward, The linear form of numbers represented by a homogeneous polynomial in any number of variables, Ann. of Math. (2) 33 (1932), no. 2, 324–326. MR 1503056, DOI 10.2307/1968334 On the behaviour of non-static models of the universe when the cosmological term is omitted, (with R. C. Tolman), Phys. Rev. 39 (1932), 835-843.
- Morgan Ward, A Type of Multiplicative Diophantine System, Amer. J. Math. 55 (1933), no. 1-4, 67–76. MR 1506944, DOI 10.2307/2371110 A property of recurring series, Proc. Nat. Acad. Sci. U.S.A. 19 (1933), 914-916.
- Morgan Ward, The cancellation law in the theory of congruences to a double modulus, Trans. Amer. Math. Soc. 35 (1933), no. 1, 254–260. MR 1501682, DOI 10.1090/S0002-9947-1933-1501682-6
- Morgan Ward, The arithmetical theory of linear recurring series, Trans. Amer. Math. Soc. 35 (1933), no. 3, 600–628. MR 1501705, DOI 10.1090/S0002-9947-1933-1501705-4
- Morgan Ward, Questions, Discussions, and Notes: A Certain Class of Trigonometric Integrals, Amer. Math. Monthly 40 (1933), no. 6, 340–346. MR 1522833, DOI 10.2307/2301523
- Morgan Ward, The Representation of Stirling’s Numbers and Stirling’s Polynomials as Sums of Factorials, Amer. J. Math. 56 (1934), no. 1-4, 87–95. MR 1507004, DOI 10.2307/2370916
- Morgan Ward, Questions, Discussions, and Notes: On the Vanishing of the Sum of the $N$th Powers of the Roots of a Cubic Equation, Amer. Math. Monthly 41 (1934), no. 5, 313–316. MR 1523091, DOI 10.2307/2300994
- Morgan Ward, Note on the period of a mark in a finite field, Bull. Amer. Math. Soc. 40 (1934), no. 4, 279–281. MR 1562836, DOI 10.1090/S0002-9904-1934-05847-6 Note on an arithmetical property of recurring series, Math. Z. 39 (1934), 211-214.
- Morgan Ward, An arithmetical property of recurring series of the second order, Bull. Amer. Math. Soc. 40 (1934), no. 12, 825–828. MR 1562981, DOI 10.1090/S0002-9904-1934-05972-X
- Morgan Ward, Note on the iteration of functions of one variable, Bull. Amer. Math. Soc. 40 (1934), no. 10, 688–690. MR 1562953, DOI 10.1090/S0002-9904-1934-05942-1 The numerical evaluation of a class of trigonometric series, Amer. Math. Monthly 41 (1934), 563-565.
- Morgan Ward, An enumerative problem in the arithmetic of linear recurring series, Trans. Amer. Math. Soc. 37 (1935), no. 3, 435–440. MR 1501795, DOI 10.1090/S0002-9947-1935-1501795-0
- Morgan Ward, A Determination of all Possible Systems of Strict Implication, Amer. J. Math. 57 (1935), no. 2, 261–266. MR 1507068, DOI 10.2307/2371202 Conditions for factorization in a set closed under a single operation, Ann. of Math. (2) 36 (1935), 36-39.
- Morgan Ward, On the factorization of polynomials to a prime modulus, Ann. of Math. (2) 36 (1935), no. 4, 870–874. MR 1503257, DOI 10.2307/1968592 The diophantine equation ${X^2} - D{Y^2} = {Z^m}$, Trans. Amer. Math. Soc. 38 (1935), 447-457.
- Morgan Ward, A Calculus of Sequences, Amer. J. Math. 58 (1936), no. 2, 255–266. MR 1507149, DOI 10.2307/2371035
- Morgan Ward and F. B. Fuller, The continuous iteration of real functions, Bull. Amer. Math. Soc. 42 (1936), no. 6, 393–396. MR 1563308, DOI 10.1090/S0002-9904-1936-06311-1
- Morgan Ward, The null divisors of linear recurring series, Duke Math. J. 2 (1936), no. 3, 472–476. MR 1545940, DOI 10.1215/S0012-7094-36-00240-5
- Morgan Ward, Note on divisibility sequences, Bull. Amer. Math. Soc. 42 (1936), no. 12, 843–845. MR 1563448, DOI 10.1090/S0002-9904-1936-06435-9
- Morgan Ward, Linear divisibility sequences, Trans. Amer. Math. Soc. 41 (1937), no. 2, 276–286. MR 1501902, DOI 10.1090/S0002-9947-1937-1501902-1
- Morgan Ward, Arithmetic functions on rings, Ann. of Math. (2) 38 (1937), no. 3, 725–732. MR 1503363, DOI 10.2307/1968611
- Morgan Ward, Some Arithmetical Applications of Residuation, Amer. J. Math. 59 (1937), no. 4, 921–926. MR 1507292, DOI 10.2307/2371358
- Morgan Ward, Residuation in structures over which a multiplication is defined, Duke Math. J. 3 (1937), no. 4, 627–636. MR 1546017, DOI 10.1215/S0012-7094-37-00351-X
- Morgan Ward, Arithmetical properties of sequences in rings, Ann. of Math. (2) 39 (1938), no. 1, 210–219. MR 1503399, DOI 10.2307/1968724 Residuated lattices, Proc. Nat. Acad. Sci. U.S.A. 24 (1938), 162-164.
- Morgan Ward, The law of apparition of primes in a Lucasian sequence, Trans. Amer. Math. Soc. 44 (1938), no. 1, 68–86. MR 1501963, DOI 10.1090/S0002-9947-1938-1501963-0
- Morgan Ward, Structure residuation, Ann. of Math. (2) 39 (1938), no. 3, 558–568. MR 1503424, DOI 10.2307/1968634
- Morgan Ward, A note on divisibility sequences, Bull. Amer. Math. Soc. 45 (1939), no. 4, 334–336. MR 1563977, DOI 10.1090/S0002-9904-1939-06980-2
- Morgan Ward and R. P. Dilworth, Evaluations over residuated structures, Ann. of Math. (2) 40 (1939), no. 2, 328–338. MR 1503460, DOI 10.2307/1968921
- Morgan Ward and R. P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939), no. 3, 335–354. MR 1501995, DOI 10.1090/S0002-9947-1939-1501995-3
- Morgan Ward, The algebra of lattice functions, Duke Math. J. 5 (1939), no. 2, 357–371. MR 1546130, DOI 10.1215/S0012-7094-39-00531-4
- Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
- Morgan Ward, A characterization of Dedekind structures, Bull. Amer. Math. Soc. 45 (1939), no. 6, 448–451. MR 1564002, DOI 10.1090/S0002-9904-1939-07005-5
- Morgan Ward, Note on the general rational solution of the equation $ax^2-by^2=z^3$, Amer. J. Math. 61 (1939), 788–790. MR 23, DOI 10.2307/2371337
- Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944
- Garrett Birkhoff and Morgan Ward, A characterization of Boolean algebras, Ann. of Math. (2) 40 (1939), 609–610. MR 9, DOI 10.2307/1968945
- Morgan Ward, Residuated distributive lattices, Duke Math. J. 6 (1940), 641–651. MR 2845 The arithmetical properties of modular lattices, Rev. Ci. Lima 430 (1941), 593-603.
- Morgan Ward, The closure operators of a lattice, Ann. of Math. (2) 43 (1942), 191–196. MR 6144, DOI 10.2307/1968865
- Morgan Ward, Euler’s three biquadrate problem, Proc. Nat. Acad. Sci. U.S.A. 31 (1945), 125–127. MR 12104, DOI 10.1073/pnas.31.4.125
- Morgan Ward, Memoir on elliptic divisibility sequences, Amer. J. Math. 70 (1948), 31–74. MR 23275, DOI 10.2307/2371930
- Morgan Ward, Euler’s problem on sums of three fourth powers, Duke Math. J. 15 (1948), 827–837. MR 27287
- Morgan Ward, The law of repetition of primes in an elliptic divisibility sequence, Duke Math. J. 15 (1948), 941–946. MR 27286
- Morgan Ward, Mathematical Notes: A Generalized Integral Test for Convergence of Series, Amer. Math. Monthly 56 (1949), no. 3, 170–172. MR 1527199, DOI 10.2307/2305031
- R. P. Dilworth and Morgan Ward, Note on a paper by C. E. Rickart, Bull. Amer. Math. Soc. 55 (1949), 1141. MR 32579, DOI 10.1090/S0002-9904-1949-09342-4
- Morgan Ward, Arithmetical properties of the elliptic polynomials arising from the real multiplication of the Jacobi functions, Amer. J. Math. 72 (1950), 284–302. MR 33857, DOI 10.2307/2372033
- Morgan Ward, Arithmetical properties of polynomials associated with the lemniscate elliptic functions, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 359–362. MR 36776, DOI 10.1073/pnas.36.6.359
- Morgan Ward, A class of soluble Diophantine equations, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 113–114. MR 41870, DOI 10.1073/pnas.37.2.113
- Morgan Ward, Prime divisors of second order recurring sequences, Duke Math. J. 21 (1954), 607–614. MR 64073
- Morgan Ward, The maximal prime divisors of linear recurrences, Canadian J. Math. 6 (1954), 455–462. MR 66408, DOI 10.4153/CJM-1954-047-9
- Morgan Ward, Cyclotomy and the converse of Fermat’s theorem, Amer. Math. Monthly 61 (1954), 564. MR 63397, DOI 10.2307/2307608
- Morgan Ward, The intrinsic divisors of Lehmer numbers, Ann. of Math. (2) 62 (1955), 230–236. MR 71446, DOI 10.2307/1969677
- Morgan Ward, On the number of vanishing terms in an integral cubic recurrence, Amer. Math. Monthly 62 (1955), 155–160. MR 67136, DOI 10.2307/2306618
- Morgan Ward, The laws of apparition and repetition of primes in a cubic recurrence, Trans. Amer. Math. Soc. 79 (1955), 72–90. MR 68579, DOI 10.1090/S0002-9947-1955-0068579-7
- Morgan Ward, The mappings of the positive integers into themselves which preserve division, Pacific J. Math. 5 (1955), 1013–1023. MR 75968
- Morgan Ward, Tests for primality based on Sylvester’s cyclotomic numbers, Pacific J. Math. 9 (1959), 1269–1272. MR 108464
- Morgan Ward, The vanishing of the homogeneous product sum of the roots of a cubic, Duke Math. J. 26 (1959), 553–562. MR 110669 Some diophantine problems connected with linear recurrences, Report of the Institute in the Theory of Numbers, Univ. Colorado, Boulder, Colorado, 1959, pp. 250-257.
- Morgan Ward, The vanishing of the homogeneous product sum on three letters, Duke Math. J. 27 (1960), 619–624. MR 114790
- Morgan Ward, The calculation of the complete elliptic integral of the third kind, Amer. Math. Monthly 67 (1960), 205–213. MR 136053, DOI 10.2307/2309677
- Morgan Ward, The prime divisors of Fibonacci numbers, Pacific J. Math. 11 (1961), 379–386. MR 138586
- Morgan Ward, The linear $p$-adic recurrence of order two, Illinois J. Math. 6 (1962), 40–52. MR 138585
- E. C. Dade, D. W. Robinson, O. Taussky, and M. Ward, Divisors of recurrent sequences, J. Reine Angew. Math. 214(215) (1964), 180–183. MR 161875, DOI 10.1515/crll.1964.214-215.180
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 61 (1993), 307-311
- MSC: Primary 01A70; Secondary 11-03
- DOI: https://doi.org/10.1090/S0025-5718-1993-1182245-3
- MathSciNet review: 1182245