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Abelian Groups and Modules: Proceedings of the Padova by Toma Albu, Patrick F. Smith (auth.), Alberto Facchini,

By Toma Albu, Patrick F. Smith (auth.), Alberto Facchini, Claudia Menini (eds.)

On the twenty sixth of November 1992 the organizing committee amassed 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 saved up via another assembly. in view that that first time it used to be transparent to us that our objective was once no longer really easy. actually the most meant issues of abelian teams, modules over commutative earrings and non commutative earrings became so really good within the final years that it appeared fairly formidable to slot them into just one assembly. besides, in view that all people folks shared an analogous mathematical roots, we did are looking to emphasize a typical hyperlink. So we elaborated the lengthy symposium time table: 3 days of abelian teams and 3 days of modules over non commutative jewelry with a days' bridge of commutative algebra in among. a number of the 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 large viewers for an Algebra assembly. Now that the assembly is over, we will say that our preliminary feeling was once right.

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S. Roumanie 23 (71) (1979), 115-116. 2. T. ALBU and C. NAsTAsESCU, Decompositions primaires dans les categories de Grothendieck commutatives I, J. Reine Angew. Math. 280 (1976), 172-194. 3. T. ALBU and C. NAsTAsESCU, Decompositions primaires dans les categories de Grothendieck commutatives II, J. Reine Angew. Math. 282 (1976), 172-185. 4. T. ALBU and C. , New York and Basel, 1984. 5. T. ALBU and P. F. SMITH, Localization of modular lattices, Krull dimension, and the Hopkins-Levitzki Theorem (I), University of Glasgow, Department of Mathematics, Preprint Series, Paper No.

Linearly compact commutative rings are (finite) products of local ones (Zelinsky [90]). Every linearly compact local noetherian ring is obviously complete and complete local rings are described by Cohen [22] using power series rings. The structure of linearly compact valuation domains was investigated by Kaplansky [44]. He proved that, up to a smaller, still unknown class, they are generalized power series rings over fields. All rings with AB5* are semiperfect (Lemonnier [54]). Almost all of them are linearly compact from the following unpublished result of Vamos: if the module R(R EB R) satisfies AB5*, then R is linearly compact.

This paper is devoted to a survey of some recent, albeit limited, results on near isomorphism and isomorphism at p (the local case of near isomorphism) for Butler groups. As discussed in Section 2, there is reason to believe that near isomorphism is the "right" equivalence relation to study, being more tractable than isomorphism while retaining more of the group structure (such as indecomposability) than quasiisomorphism. 1). For these representation categories, little seems to be known about representation type.

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