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Hussain, Fawad
- Congruences and External Direct Sum of LA-Modules
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Authors
Affiliations
1 Department of Mathematics, Hazara University, Mansehra, KPK - 21310, PK
2 Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad - 22010, PK
1 Department of Mathematics, Hazara University, Mansehra, KPK - 21310, PK
2 Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad - 22010, PK
Source
Indian Journal of Science and Technology, Vol 8, No 28 (2015), Pagination:Abstract
In this paper we study a new algebraic structure namely left almost module (LA-module in short). We extend the notion of congruences to LA-modules which is defined in1 for semigroups. We show that every homomorphism defines a congruence relation on LA-modules and prove analogues of isomorphism theorems. We also define external direct sum of LA-modules and show that the internal direct sum of LA-submodules is isomorphic to the external direct sum of those LA-submodules.Keywords
Congruences, External Direct Sums, Internal Direct Sums, LA-Modules, LA-Module Homomorphism, LA-Sub Modules- Quotient Seminear-Rings
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Authors
Affiliations
1 Department of Mathematics, Abbottabad University of Science and Technology, PK
2 Department of Mathematics, Hazara University Mansehra, PK
1 Department of Mathematics, Abbottabad University of Science and Technology, PK
2 Department of Mathematics, Hazara University Mansehra, PK