Morphic objects in categories

Room 0.06, Mathematics building, FCUP
Friday, 16 November, 2012 - 15:00

A left R-module M is called morphic if M/im(f) is isomorphic to ker(f), for every endomorphism f of M, that is if the dual of the Nöther isomorphism theorem holds.

Having as a starting point the categorial definition of morphic object given by Professor Grigore Calugareanu in the article "Morphic abelian groups" we recover most of its proprieties under suitable conditions.

In 1976 Erlich proved that an endomorphism f of a module M is unit regular if and only if it is regular and M/im(f) is isomorphic to ker(f)\alpha. After nearly 30 years, the interest for this dual florished in 2003-2004 when Nicholson and Sánchez Campos publised a series of papers and nowadays the subject continues to be investigated. In this paper, some results are generalized in so called Puppe-exact categories (exact by Mitchell and Herrlich, Strecker) and most of them are recovered in abelian categories. We also discuss how the Mitchell Embedding Theorem can be used in order to reduce proofs from abelian categories to the categories of modules. Connection with unit regular and regular objects is made and some special examples are given together with some applications.

(this is joint work with Grigore Calugareanu)

Speaker: 

Lavinia Pop (Babeş-Bolyai, Cluj-Napoca, Romenia)
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