Fitriani, Fitriani and Emilia Wijayanti, Indah and Surodjo, Budi (2018) A Generalization of Basis and Free Modules Relatives to a Family U of R-Modules. Journal of Physics: Conference Series, 1097 (012087). pp. 1-7. ISSN 1742-6588 (Print) 1742-6596 (Online)

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Let U be a family of R-modules and V be a submodule of a direct sum of some elements in U. The aim of this paper is to generalize basis and free modules. We use the concept of U v-generated module and X-sublinearly independent to provide the definition of U-basis and U-free module. We construct a U -basis of an R-module M as a pair (X, V), which a family U is X-sub-linearly independent to M and M is a Uv-generated module. Furthermore, we define U -basis of M as a U -basis which has the maximal element on the first component and the minimal element on the second component of a pair (X, V). The results show that the first component of (X, V) in U -basis is closed under submodules and intersections. Moreover, we prove that the second component of (X, V) in U -basis is closed under direct sums. We also determine some U -free modules related to a family U which contains all Z-module Z modulo p power of n, where p prime and n  2.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika
Date Deposited: 06 Nov 2018 03:06
Last Modified: 06 Nov 2018 03:06

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