FACTOR CATEGORIES AND INFINITE DIRECT SUMS

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International Electronic Journal of Algebra
Volume:5 Issue:5
FACTOR CATEGORIES AND INFINITE DIRECT SUMS

FACTOR CATEGORIES AND INFINITE DIRECT SUMS

Authors : Alberto FACCHİNİ, Pavel PŘÍHODA

Pages : 135-168

View : 14 | Download : 10

Publication Date : 2009-06-01

Article Type : Research Paper

Abstract :We give an improved categorical version of the Weak Krull-Schmidt Theorem for serial modules proved by the second author in [10]. The main improvement consists in the fact that it applies not only to serial modules, but also, more generally, to arbitrary direct summands of serial modules. The technique is based on categorical methods, essentially representing the category addinsert ignore into journalissuearticles values(SUsr); of direct summands of serial modules into factors of the category addinsert ignore into journalissuearticles values(SUsr); modulo suitable ideals, one for each uniserial module of type 1 and two for each uniserial module of type 2. Our categorical technique can be applied to further broader settings.
Keywords : Uniserial modules, serial modules, direct sum decompositions

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