A GENERALIZATION OF CORETRACTABLE MODULES
Publish place: Journal of Algebraic Systems، Vol: 5، Issue: 2
Publish Year: 1397
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JAS-5-2_007
تاریخ نمایه سازی: 18 تیر 1398
Abstract:
Let $R$ be a ring and $M$ a right $R$-module. We call $M$, coretractable relative to $overline{Z}(M)$ (for short, $overline{Z}(M)$-coretractable) provided that, for every proper submodule $N$ of $M$ containing $overline{Z}(M)$, there is a nonzero homomorphism $f:dfrac{M}{N}rightarrow M$. We investigate some conditions under which the two concepts coretractable and $overline{Z}(M)$-coretractable, coincide. For a commutative semiperfect ring $R$, we show that $R$ is $overline{Z}(R)$-coretractable if and only if $R$ is a Kasch ring. Some examples are provided to illustrate different concepts.
Authors
A. R. Moniri Hamzekolaee
Department of Mathematics, University of Mazandaran, Babolsar, Iran