•Journal•ISSN: 1509-9415
Discussiones Mathematicae General Algebra and Applications
De Gruyter Open
About: Discussiones Mathematicae General Algebra and Applications is an academic journal published by De Gruyter Open. The journal publishes majorly in the area(s): Distributive property & Semigroup. It has an ISSN identifier of 1509-9415. It is also open access. Over the lifetime, 387 publications have been published receiving 1125 citations. The journal is also known as: DMGAA.
Papers published on a yearly basis
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TL;DR: The Horadam hybrid numbers are introduced and some their properties are given: Binet formula, character and generating function.
Abstract: Abstract In this paper we introduce the Horadam hybrid numbers and give some their properties: Binet formula, character and generating function.
45 citations
TL;DR: In this article, the Cayley-Dickson process was applied to the subalgebra structure of the sedenion algebra S and its zero divisors, and it was shown that S has subalgebras isomorphic to R; C; H; O; and a newly identifled algebra e O called the quasi-octonions that contains the zero-divisors of S.
Abstract: The algebrasC (complex numbers), H (quaternions), andO (octonions) are real division algebras obtained from the real numbers R by a doubling procedure called the Cayley-Dickson Process. By doubling R (dim 1), we obtain C (dim 2); then C produces H (dim 4); and H yields O (dim 8): The next doubling process applied to O then yields an algebra S (dim 16) called the sedenions. This study deals with the subalgebra structure of the sedenion algebra S and its zero divisors. In particular, it shows that S has subalgebras isomorphic to R; C; H; O; and a newly identifled algebra e O called the quasi-octonions that contains the zero-divisors of S:
34 citations
TL;DR: In this article, the concept of pseudo BE-algebra is introduced and it is proved that every pseudo filter is an union of pseudo upper sets. But it is not known whether a pseudo filter can be a pseudo subalgebra.
Abstract: In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and preimage of a pseudo filter is also a pseudo filter. Furthermore, the notion 96 R.A. Borzooei, A. Borumand Saeid, A. Rezaei, A. Radfar and ... of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.
29 citations
TL;DR: In this paper, a bounded lattice L = (L;∨,∧, 0, 1), where for each p ∈ L there exists an antitone involution on the interval [p, 1], was introduced and characterized by simple axioms similar to that of Abbott's implication algebra.
Abstract: We introduce a bounded lattice L = (L;∨,∧, 0, 1), where for each p ∈ L there exists an antitone involution on the interval [p, 1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L; ·, 0) (the assigned algebra to L) and we characterizeA(L) by simple axioms similar to that of Abbott’s implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by L or A(L) to obtain all axioms of MV-algebra.
26 citations
TL;DR: In this paper, the authors introduce some new classes of UP-algebras related to semigroups, called a left UPsemigroup, a right UP-semigroup and a fully-upsemigroup.
Abstract: In this paper, we introduce some new classes of algebras related to UP-algebras and semigroups, called a left UP-semigroup, a right UP-semigroup, a fully UP-semigroup, a left-left UP-semigroup, a right-left UP-semigroup, a left-right UP-semigroup, a right-right UP-semigroup, a fully-left UP-semigroup, a fully-right UP-semigroup, a left-fully UP-semigroup, a right-fully UP-semigroup, a fully-fully UP-semigroup, and find their examples.
25 citations