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Acta Mathematica Hungarica

, Volume 158, Issue 1, pp 202–215 | Cite as

Uniqueness of primary decompositions in Laskerian le-modules

  • A. K. Bhuniya
  • M. KumbhakarEmail author
Article
  • 26 Downloads

Abstract

We introduce and study a new algebraic structure, which we call le-modules. An le-module M over a commutative ring R is a complete lattice ordered monoid (M, + ,⩽,e) with greatest element e and module like action of R on it. Our motivation comes from abstract ideal theory and the theory of lattice modules, and with a desire to develop an alternative abstract submodule theory. An le-module M over R abstracts the set of all subsets of a module over R and submodules are characterized as distinguished elements in M. Here we introduce prime and primary elements in an le-module and establish two uniqueness theorems for primary decompositions of a submodule element in a Laskerian le-module.

Mathematics Subject Classification

13C99 06F25 

Key words and phrases

le-module submodule element prime radical primary decomposition 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of MathematicsVisva-BharatiSantiniketanIndia
  2. 2.Department of MathematicsNistarini CollegePuruliaIndia

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