• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.2
• /
• pp.179-189
• /
• 2019

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

• Kyungpook Mathematical Journal
• /
• v.56 no.3
• /
• pp.669-682
• /
• 2016

In this paper, we study the cellular structure of the G-edge colored partition algebras, when G is a finite group. Further, we classified all the irreducible representations of these algebras using their cellular structure whenever G is a finite cyclic group. Also we prove that the ${\mathbb{Z}}/r{\mathbb{Z}}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.

• Journal of applied mathematics & informatics
• /
• v.40 no.1_2
• /
• pp.133-139
• /
• 2022

We offered a new method for constructing Latin squares. We introduce the concept of a standard form via example for Latin squares of order n and we also call it symmetric BCL algebras matrix, and thereby become BCL algebra representations of the picture of Latin squares. Our research shows that some new properties of the Latin squares with BCL algebras are in ℤ_n.

• Journal of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.289-297
• /
• 2010

By using as main tool the theory of prime submodules this article is devoted to describing the structure of the minimal prime ideals of the equidimensional symmetric algebra of a finitely generated module.

• Korean Journal of Mathematics
• /
• v.29 no.2
• /
• pp.387-393
• /
• 2021

In this paper, we introduce the notion of symmetric bi-derivations on subtraction algebra and investigated some related properties. We prove that a map D : X × X → X is a symmetric bi-derivation on X if and only if D is a symmetric map and it satisfies D(x - y, z) = D(x, z) - y for all x, y, z ∈ X.

• Korean Journal of Mathematics
• /
• v.26 no.1
• /
• pp.53-60
• /
• 2018

In this paper, we consider the question of the Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra on ${\mathbb{F}}$, where ${\mathbb{F}}$ is an algebraic closed field. By using the Lie product of the basis elements of Heisenberg Lie algebras, all Rota-Baxter operators of 3-dimensional Heisenberg Lie algebras are calculated and left symmetric algebras of 3-dimensional Heisenberg Lie algebra are determined by using the Yang-Baxter operators.

• The Pure and Applied Mathematics
• /
• v.6 no.1
• /
• pp.1-8
• /
• 1999

Let $K_{\alpha}(G)$ (resp. $K_s(G)$) be the abelian (resp. symmetric) Kac algebra for a locally compact group G. We show that there exists a one-to-one correspondence between the subgroups of G and the sub-Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$). Moreover we obtain similar correspondences between the subgroups of G and the reduced Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$).

• Communications of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.209-216
• /
• 2016

In this paper, we introduce the notion of symmetric bi-derivations of a B-algebra and investigate some related properties. We study the notion of symmetric bi-derivations of a 0-commutative B-algebra and state some related properties.

• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.1-11
• /
• 2020

In this paper, we introduce the notion of symmetric bi-f-derivation of lattice implication algebra and investigated some related properties. Also, we prove that if D is a symmetric bi-f-derivation of L, then D(x → y, z) = f(x) → D(y, z) for all x, y, z ∈ L.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.4
• /
• pp.441-451
• /
• 2019

In this paper, we introduce the notion of symmetric bi-f-derivation on subtraction algebra and investigated some related properties. Also, we prove that if D : X → X is a symmetric bi-f-derivation on X, then D satisfies D(x - y, z) = D(x, z) - f(y) for all x, y, z ∈ X.