Yıl: 2024 Cilt: 5 Sayı: 1 Sayfa Aralığı: 36 - 47 Metin Dili: İngilizce DOI: 10.54974/fcmathsci.1273407 İndeks Tarihi: 26-02-2024
Dimodules
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 Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [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.
APA | Akçay E, EKİZ C (2024). Dimodules. , 36 - 47. 10.54974/fcmathsci.1273407 |
Chicago | Akçay Ertuğrul,EKİZ Canan Dimodules. (2024): 36 - 47. 10.54974/fcmathsci.1273407 |
MLA | Akçay Ertuğrul,EKİZ Canan Dimodules. , 2024, ss.36 - 47. 10.54974/fcmathsci.1273407 |
AMA | Akçay E,EKİZ C Dimodules. . 2024; 36 - 47. 10.54974/fcmathsci.1273407 |
Vancouver | Akçay E,EKİZ C Dimodules. . 2024; 36 - 47. 10.54974/fcmathsci.1273407 |
IEEE | Akçay E,EKİZ C "Dimodules." , ss.36 - 47, 2024. 10.54974/fcmathsci.1273407 |
ISNAD | Akçay, Ertuğrul - EKİZ, Canan. "Dimodules". (2024), 36-47. https://doi.org/10.54974/fcmathsci.1273407 |
APA | Akçay E, EKİZ C (2024). Dimodules. Fundamentals of contemporary mathematical sciences (Online), 5(1), 36 - 47. 10.54974/fcmathsci.1273407 |
Chicago | Akçay Ertuğrul,EKİZ Canan Dimodules. Fundamentals of contemporary mathematical sciences (Online) 5, no.1 (2024): 36 - 47. 10.54974/fcmathsci.1273407 |
MLA | Akçay Ertuğrul,EKİZ Canan Dimodules. Fundamentals of contemporary mathematical sciences (Online), vol.5, no.1, 2024, ss.36 - 47. 10.54974/fcmathsci.1273407 |
AMA | Akçay E,EKİZ C Dimodules. Fundamentals of contemporary mathematical sciences (Online). 2024; 5(1): 36 - 47. 10.54974/fcmathsci.1273407 |
Vancouver | Akçay E,EKİZ C Dimodules. Fundamentals of contemporary mathematical sciences (Online). 2024; 5(1): 36 - 47. 10.54974/fcmathsci.1273407 |
IEEE | Akçay E,EKİZ C "Dimodules." Fundamentals of contemporary mathematical sciences (Online), 5, ss.36 - 47, 2024. 10.54974/fcmathsci.1273407 |
ISNAD | Akçay, Ertuğrul - EKİZ, Canan. "Dimodules". Fundamentals of contemporary mathematical sciences (Online) 5/1 (2024), 36-47. https://doi.org/10.54974/fcmathsci.1273407 |