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Bass’s work in ring theory and projective modules. (English) Zbl 0945.16004

Lam, T. Y. (ed.) et al., Algebra, \(K\)-theory, groups, and education. On the occasion of Hyman Bass’s 65th birthday. Mainly the proceedings of the conference, Columbia University, New York, NY, November 6-7, 1997. Providence, RI: American Mathematical Society. Contemp. Math. 243, 83-124 (1999).
This very clear and interesting survey covers the work of Hyman Bass on ring theory and projective modules, done early in his career during the late 1950s and early 1960s.
The first part of the paper deals with Bass’s work on projective modules which included work on big projectives, the stable structure of projective modules, work related to Serre’s conjecture and rings with binary generated ideals (Bass rings).
In the second part, Bass’s contribution to ring theory is summarized. His work included semiperfect rings as generalizations of semiprimary rings, perfect rings and restricted DCC as well as representation theory and stable range of rings, especially rings of stable range one. Study of these concepts led up to Bass’s pioneering work on algebraic \(K\)-theory (which is not covered in this survey).
Throughout the survey, the significance of Bass’s work and the influence of his contribution on the subsequent work of other algebraists are stressed. His work is shown to have shaped the thinking of researchers in the areas covered for years.
For the entire collection see [Zbl 0928.00073].

MSC:

16D40 Free, projective, and flat modules and ideals in associative algebras
16-02 Research exposition (monographs, survey articles) pertaining to associative rings and algebras
16-03 History of associative rings and algebras
16E20 Grothendieck groups, \(K\)-theory, etc.
16L30 Noncommutative local and semilocal rings, perfect rings
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Bass, H.
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