Research Article
Year 2024,
Volume: 5 Issue: 1, 36 - 47, 31.01.2024
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.
References
- [1] Grillet P.A., Semigroups: An Introduction to the Structure Theory, Marcel Dekker, 1995.
- [2] Hungerford T.W., Algebra, Springer-Verlag, 1974.
- [3] Kilp M., Knauer U., Mikhalev A.V., Monoids, Acts and Categories with Applications to Wreath Products and Graphs, De Gruyter Expositions in Mathematics, 29, Walter de Gruyter, 2000.
- [4] Loday J.L., Dialgebras in “Dialgebras and Related Operads”, 7-66, Lecture Notes in Mathematics, 1763, Springer, 2001.
- [5] Zhuchok A.V., Commutative dimonoids, Algebra and Discrete Mathematics, 2, 116-127, 2009.
- [6] Zhuchok A.V., Dimonoids, Algebra and Logic, 50(4), 323-340, 2011.
- [7] Zhuchok A.V., Free commutative dimonoids, Algebra and Discrete Mathematics, 9, 109-119, 2010.
- [8] Zhuchok A.V., Free dimonoids, Ukrainian Mathematical Journal, 63(2), 196-208, 2011.
- [9] Zhuchok A.V., On the structure of dimonoids, Semigroup Forum, 94(2), 194-203, 2009.
Year 2024,
Volume: 5 Issue: 1, 36 - 47, 31.01.2024
Abstract
References
- [1] Grillet P.A., Semigroups: An Introduction to the Structure Theory, Marcel Dekker, 1995.
- [2] Hungerford T.W., Algebra, Springer-Verlag, 1974.
- [3] Kilp M., Knauer U., Mikhalev A.V., Monoids, Acts and Categories with Applications to Wreath Products and Graphs, De Gruyter Expositions in Mathematics, 29, Walter de Gruyter, 2000.
- [4] Loday J.L., Dialgebras in “Dialgebras and Related Operads”, 7-66, Lecture Notes in Mathematics, 1763, Springer, 2001.
- [5] Zhuchok A.V., Commutative dimonoids, Algebra and Discrete Mathematics, 2, 116-127, 2009.
- [6] Zhuchok A.V., Dimonoids, Algebra and Logic, 50(4), 323-340, 2011.
- [7] Zhuchok A.V., Free commutative dimonoids, Algebra and Discrete Mathematics, 9, 109-119, 2010.
- [8] Zhuchok A.V., Free dimonoids, Ukrainian Mathematical Journal, 63(2), 196-208, 2011.
- [9] Zhuchok A.V., On the structure of dimonoids, Semigroup Forum, 94(2), 194-203, 2009.
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | January 31, 2024 |
| Published in Issue | Year 2024 Volume: 5 Issue: 1 |
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