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Dimodules

Yıl 2024, Cilt: 5 Sayı: 1, 36 - 47, 31.01.2024

Ertuğrul Akçay Canan Akın

Öz

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.

Anahtar Kelimeler

Dimonoid Semigroup Dimodule

Kaynakça

  • [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.

Yıl 2024, Cilt: 5 Sayı: 1, 36 - 47, 31.01.2024

Ertuğrul Akçay Canan Akın

Öz

Kaynakça

  • [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.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Articles
Yazarlar

Ertuğrul Akçay 0000-0002-4515-9344

Canan Akın 0000-0002-8922-3272

Yayımlanma Tarihi 31 Ocak 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 5 Sayı: 1

Kaynak Göster

 Kapak Resmi İndir

19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.