Neal Henry McCoy explained

Neal Henry McCoy (March 6, 1905 – January 5, 2001) was an American mathematician, university professor, and author of several textbooks for mathematics undergraduates. His 1960 textbook Introduction to Modern Algebra has gone through several editions and has been translated into many foreign languages.[1]

Early life and education

McCoy was born into a homesteading family in Waukomis, Oklahoma (which was part of the Oklahoma Territory from 1890 to 1907). He had an older sister Dorothy McCoy (1903–2001), who became the first woman to receive a Ph.D. in mathematics from the University of Iowa. As an infant, he moved in 1906 with his mother and sister to Chesapeake, Missouri after the death of his father.[2] After graduating with a bachelor's degree from Baylor University,[1] he became a graduate student at the University of Iowa. There he graduated in 1929 with a Ph.D. in mathematics with adviser Edward Wilson Chittenden. McCoy's Ph.D. thesis On commutation formulas in the algebra of quantum mechanics was published in abbreviated form in the Transactions of the American Mathematical Society.[3]

Career

For two academic years from 1929 to 1931, McCoy studied at Princeton University as a National Research Fellow. He joined in 1931 the staff of the mathematics department of Northampton's Smith College,[1] There he was promoted to full professor in 1942[4] and was appointed to the Gates Chair in Mathematics in 1963, retiring as professor emeritus in 1970.[1] McCoy did research on abstract algebra, especially the theory of rings and matrices with elements in rings, and algebraic aspects of quantum mechanics.[4] From 1951 to 1954 he was the editor-in-chief of the Duke Mathematical Journal.[1] He was an associate editor for the American Mathematical Monthly and the Pi Mu Epsilon Journal.[4]

McCoy ring

In 1942, McCoy proved the following theorem:
Let R be a commutative ring with multiplicative unit, and let f(x) be a zero divisor in the polynomial ring R[x]. Then there is a nonzero element r ∈ R with f(x)r = 0.[5]
In 1997 Mangesh B. Rege and Sima Chhawchharia introduced definitions of rings,[6] which in 2006, independently and motivated by McCoy's 1942 theorem, were re-introduced by Pace P. Nielsen, who gave the concepts the names "right McCoy ring", "left McCoy ring", and "McCoy ring" (a ring which is both right McCoy and left McCoy).[7] [8]

Rings and Ideals (1948)

McCoy wrote the 8th book in the series of Carus Mathematical Monographs published by the Mathematical Association of America. The book is almost entirely self-contained.[9] In a 1948 review, André Weil praised the book for the optimized simplicity of the mathematical proofs, an "easy and readable style", and "skillful use of examples".[10] In a 1949 review, C. C. MacDuffee praised the book — "as an introduction to the powerful and highly abstract method of thinking which now characterizes modern algebra, it is a gem."[11]

Personal life

In 1929 in Iowa, Neal H. McCoy married Ardis Hollingsworth (1904–1988). Their only son, Paul Albert McCoy, was killed in 1957 at age 22 in an automobile accident.[1]

Selected publications

Articles

Books

References

  1. Web site: Collection: Neal McCoy papers | Smith College Finding Aids .
  2. Book: Green. Judy. Judy Green (mathematician). LaDuke. Jeanne. Jeanne LaDuke. McCoy, Dorothy, August 9, 1903 – November 21, 2001. January 2009. 240–241. American Mathematical Society. Pioneering Women in American Mathematics: The Pre-1940 PhD's. Pioneering Women in American Mathematics. https://books.google.com/books?id=IRbOAwAAQBAJ&pg=PA240. Reprinted in Web site: From Apples to WACS: A Supplement to the Second Edition of Hale County, Texas, Bibliography. John. Sigwald. January 2016. S52–S53. Unger Memorial Library. Plain view, Texas. 2020-03-25. See also more detailed biography on pp. 399–401 of Supplementary material for Pioneering Women in American Mathematics.
  3. 10.1090/s0002-9947-1929-1501512-1 . On commutation formulas in the algebra of quantum mechanics . 1929 . McCoy . Neal H. . Transactions of the American Mathematical Society . 31 . 4 . 793–806 .
  4. Neal Henry McCoy, Associate Editor. Pi Mu Epsilon Journal . April 1952. 1. 6. 230.
  5. McCoy, N. H.. Remarks on divisors of zero. American Mathematical Monthly. 49. 286–295. 1942.
  6. Rege, M. B.. Chhawchharia, S.. Armendariz rings. Proc. Japan Acad. Ser. A Math. Sci.. 73. 1997. 1. 14–17.
  7. Nielsen, Pace P.. 2006. Semi-commtativity and the McCoy condition. Journal of Algebra. 298. 1. 134–141.
  8. J. Korean Math. Soc.. 50. 2013. 5. 959–972. On a generalization of McCoy rings. Camillo, Victor. Kwak, Tai Keun. Lee, Yang.
  9. Web site: Rings and Ideals by N. H. McCoy. Bookstore, American Mathematical Society.
  10. Weil, André. review of Rings and Ideals by Neal H. McCoy. Science. April 22, 1948. 109. 2834. 428. 10.1126/science.109.2834.428.a.
  11. MacDuffee, C. C.. Review: Rings and Ideals by N. H. McCoy. Bulletin of the American Mathematical Society. September 1949. 864–866.

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