Dimodules

Abstract

This paper introduces a new algebraic structure called dimodule. This structure is similar to a module. A dimodule occurs on a semigroup and a dimonoid in place of an additive abeliangroup and a ring, respectively. This paper presents some algebraic properties of the dimodules and supplies some of their examples. We suggest a denition of a distributive dimonoid. This paper includes examples of this notion that a distributive dimonoid does not have to be a commutative and idempotent dimonoid. We also have examples of dimonoids and dimonoid homomorphisms.

Keywords

• Dimonoid
• Semigroup
• Dimodule

References

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