Indian Journal of Science and Technology
Year: 2015, Volume: 8, Issue: 28, Pages: 1-7
Fawad Hussain1, Muhammad Sajjad Ali Khan1, Khaista Rahman1 and Madad Khan2
1 Department of Mathematics, Hazara University, Mansehra, KPK - 21310, Pakistan; [email protected], [email protected], [email protected]
2 Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad - 22010, Pakistan; [email protected]
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-submodules
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