A novel study on the structure of left almost hypermodules

Abstract

The concept of left almost hypermodule evolves as a novel extension in the field of abstract algebra, specifically within the broader framework of hypermodules. The left almost hypermodule is characterized by a set endowed with two operations, evincing properties that extends across traditional module theory and hypermodules. This abstract intents to provide a succinct overview of salient attributes and prospective implications of the left almost hypermodule, stimulating further exploration of its properties and applications. The paper provides a new definition of hypermodule that acts on the left almost hyperring, referred to as left almost hypermodule (abbreviated as LA-hypermodule), and provides some examples of this new structure. We further examine the variations between hypermodules and left almost hypermodules. By using the concept of left almost polygroups, we explore the transition from left almost polygroup to a left almost hypermodule over left almost hyperring. Lastly, we observe the outcomes in connection to homomorphism and regular relations on left almost hypermodules.

Keywords: Homomorphism on left almost hypermodule; Left almost hypermodule; Regular relations.