By Toma Albu, Patrick F. Smith (auth.), Alberto Facchini, Claudia Menini (eds.)
On the twenty sixth of November 1992 the organizing committee collected jointly, at Luigi Salce's invitation, for the 1st time. The culture of abelian teams and modules Italian meetings (Rome seventy seven, Udine eighty five, Bressanone ninety) had to be stored up by means of another assembly. on account that that first time it was once transparent to us that our aim was once now not really easy. actually the most meant themes of abelian teams, modules over commutative earrings and non commutative earrings became so really expert within the final years that it appeared relatively formidable to slot them into just one assembly. besides, for the reason that all people folks shared a similar mathematical roots, we did are looking to emphasize a typical hyperlink. So we elaborated the lengthy symposium agenda: 3 days of abelian teams and 3 days of modules over non commutative jewelry with a days' bridge of commutative algebra in among. the various most renowned names in those fields took half to the assembly. Over a hundred and forty individuals, either attending and contributing the 18 major Lectures and sixty four Communications (see record on web page xv) supplied a very broad viewers for an Algebra assembly. Now that the assembly is over, we will be able to say that our preliminary feeling used to be right.
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Extra resources for Abelian Groups and Modules: Proceedings of the Padova Conference, Padova, Italy, June 23–July 1, 1994
K. R. Fuller and Weimin Xue: On distributive modules and locally distributive rings, Chinese Ann. Math. Ser. B 12 (1991), 16-32. P. Gabriel: Des categories abeliennes, Bull. Soc. Math. France 90 (1962), 323-348. R. Goblot: Sur les anneaux lineairement compacts, C. R. Acad. Sci. Paris 270 (1970), A12121215. J. L. G6mez Pardo: Counterinjective modules and duality, J. pure appl. Algebra 61 (1989), 165-179. J. L. Gomez Pardo and P. A. Guil Asensio: QF-3 rings and Morita duality, Comm. Algebra 19 (1991), 2097-2112.
In fact, if a duality is representable by a bimodule RUs, then the domain of duality consists exactly of those modules which are isomorphic to their second U-duals. , on the concrete duality functors (Muller ). Therefore one obtains more restrictive and interesting classes of rings with duality by specializing both the reflexive modules or the bimodules RUS. Indeed, the case R = U yields the class of generalized quasi-Frobenius rings. In addition to this condition, if all reflexive modules are finitely generated, then the rings must be quasi-Frobenius (Dieudonne ).
7. 4 to the triple (R,R RR, R), one obtains the characterizations of generalized quasi-Frobenius rings given in Anh . e. a left injective cogenerator ring) which is not a two-sided P F -ring, answering a question of Azumaya  in the negative. 4 and classical descriptions of quasi-Frobenius rings, one can ask a stronger question: is a left PF-ring a generalized quasi-Frobenius ring, provided that RR satisfies AB5*, or even RR is linearly compact? We mention here a famous question of Faith: is everyone-sided injective perfect ring or even every semiprimary one-sided injective ring quasi-Frobenius?