On the existing of fully invariant submodule

Prasetyo, Puguh Wahyu and Widayati, M.Sc, Dra and Yuwaningsih, Dian Ariesta (2019) On the existing of fully invariant submodule. [Artikel Dosen]

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Abstract

Let M be a nonzero R−module, where R is a ring. A submodule U of M is called a fully invariant submodule if f(U) ⊆ U for every f 2 S, where S = EndR(M). Moreover, M is called an ⊕−supplemented module if every submodule N of M there exists a submodule K of M such that K is a direct summand of M, M = N +K, and N \K is small in M. Furthermore, M is called a cms−module if for every cofinite submodule K of M, there exist submodules P and Q of M such that P is a supplement of K, P + Q = M, and P \ Q is a small submodule in Q. In fact, factor module of a ⊕−supplemented module (respectively, cms−module) is not ⊕−supplemented (respectively, is not cms) in general. In this paper, we show that factor module of ⊕−supplemented module (respectively, cms−module) determined by fully invariant submodule is also ⊕−supplemented (respectively, cms). Moreover, we generate a fully invariant submodule by using radical of a module.

Item Type:	Artikel Dosen
Subjects:	Q Science > QA Mathematics
Divisi / Prodi:	Faculty of Teacher Training and Education (Fakultas Keguruan dan Ilmu Pendidikan) > S1-Mathematics Education (S1-Pendidikan Matematika)
Depositing User:	Dian Ariesta Yuwaningsih
Date Deposited:	23 May 2022 03:13
Last Modified:	23 May 2022 03:13
URI:	http://eprints.uad.ac.id/id/eprint/35043

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