Extensions of weakly supplemented modules | Zendy

Rafai̇l Ali̇zade | Zendy; Engı̇n Büyükaşık | Zendy

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Extensions of weakly supplemented modules

Author(s) -

Rafai̇l Ali̇zade,

Engı̇n Büyükaşık

Publication year - 2008

Publication title -

mathematica scandinavica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.553

H-Index - 30

eISSN - 1903-1807

pISSN - 0025-5521

DOI - 10.7146/math.scand.a-15075

Subject(s) - mathematics , extension (predicate logic) , commutative ring , simple (philosophy) , commutative property , ring (chemistry) , product (mathematics) , pure mathematics , direct product , discrete mathematics , combinatorics , geometry , chemistry , computer science , programming language , philosophy , organic chemistry , epistemology

It is shown that weakly supplemented modules need not be closed under extension (i.e. if U and M/U are weakly supplemented then M need not be weakly supplemented). We prove that, if U has a weak supplement in M then M is weakly supplemented. For a commutative ring R, we prove that R is semilocal if and only if every direct product of simple R-modules is weakly supplemented.

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