TY - JOUR ID - 1717 TI - $H$-supplemented modules and singularity JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - Moniri Hamzekolaee, Ali Reza AD - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar Y1 - 2020 PY - 2020 VL - 7 IS - 1 SP - 49 EP - 57 KW - $delta$-$H$-supplemented module KW - $delta$-small submodule KW - $H$-supplemented module DO - 10.22034/as.2020.1717 N2 - Let $M$ be a module over a ring $R$. We call $M$,$\delta$-$H$-supplemented provided for every submodule $N$ of $M$ there is a direct summand $D$ of $M$ such that $M=N+X$ if and only if $M=D+X$ for every submodule $X$ of $M$ with $M/X$ singular. We prove that $M$ is $\delta$-$H$-supplemented if and only if for every submodule $N$ of $M$ there exists a direct summand $D$ of $M$ such that $(N+D)/N\ll_{\delta} M/N$ and $(N+D)/D\ll_{\delta} M/D$. UR - https://as.yazd.ac.ir/article_1717.html L1 - https://as.yazd.ac.ir/article_1717_57059068e17920865933936d97025ae6.pdf ER -