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Title : Category of Submodules of a Uniserial Module
Author :

Fitriani (1) Prof. Dr.rer.nat. Indah Emilia Wijayanti, S.Si., M.Si. (2) Dr. Budi Surodjo, M.Si. (3) Prof. Dr. Sri Wahyuni, S.U. (4) Ahmad Faisol (5)
Date : 30 2021
Keyword : Sub-exact Sequences, Pre-additive Category, Uniserial Module Sub-exact Sequences, Pre-additive Category, Uniserial Module
Abstract : Let R be a ring, K,M be R-modules, L a uniserial R-module, and X a submodule of L. The triple (K,L,M) is said to be X-sub-exact at L if the sequence K→X→M is exact. Let σ(K,L,M) is a set of all submodules Y of L such that (K,L,M) is Y -sub-exact. The sub-exact sequence is a generalization of an exact sequence. We collect all triple (K,L,M) such that (K,L,M) is an X-sub exact sequence, where X is a maximal element of σ(K,L,M). In a uniserial module, all submodules can be compared under inclusion. So, we can find the maximal element of σ(K,L,M). In this paper, we prove that the set σ(K,L,M) form a category, and we denoted it by CL. Furthermore, we prove that CY is a full subcategory of CL, for every submodule Y of L. Next, we show that if L is a uniserial module, then CL is a pre-additive category. Every morphism in CL has kernel under some conditions. Since a module factor of L is not a submodule of L, every morphism in a category CL does not have a cokernel. So, CL is not an abelian category. Moreover, we investigate a monic X-sub-exact and an epic X-sub-exact sequence. We prove that the triple (K,L,M) is a monic X-sub-exact if and only if the triple Z-modules (, , ) is a monic -sub-exact sequence, for all R-modules N. Furthermore, the triple (K,L,M) is an epic X-sub-exact if and only if the triple Z-modules (, , ) is a monic -sub-exact, for all R-module N.
Group of Knowledge : Matematika
Original Language : English
Level : Internasional
Status :
Published
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1 Category of Submodules of a Uniserial Module.pdf
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2 Dokumen-Lengkap-Category-----.pdf
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3 Scopus - Document details - Category of submodules of a uniserial module _ Signed in.pdf
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4 Scimago-jurnal_2099575_c52170772c90d5451549c239681ea808.pdf
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5 Category of submodules of a uniserial module.pdf
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