• Communications of the Korean Mathematical Society
• /
• v.10 no.1
• /
• pp.123-131
• /
• 1995

The notion of our non-associative algebra is obtained from the Lotka-Volterra system of differential equation describing competitiion between animals or vegetals species and also in the kinetic theory of gasses. For the structure of an algebra, the existence of idempotents is of particular interest. But also from the biological aspect the existence of such elements is of interest because the equilibria of a population which can be described by an algebra correspond to idempotents of this algebra. Thus we present some properties of the general natures for a Lotka-Volterra algebra associated to a weight function and idempotents elements.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.241-246
• /
• 2007

For the evaluation algebra $F[e^{{\pm}x}]_M\;if\;M=\{{\partial}\}$, then $$Der_{non}(F[e^{{\pm}x}]_M)$$ of the evaluation algebra $(F[e^{{\pm}x}]_M)$ is found in the paper [15]. For $M=\{{\partial},\;{\partial}^2\}$, we find $Der_{non}(F[e^{{\pm}x}]_M))$ of the evaluation algebra $F[e^{{\pm}x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.527-541
• /
• 2001

We find the necessary and sufficient conditions for the smash product algebra structure and the crossed coproduct coalgebra structure with th dual cocycle $\alpha$ to afford a Hopf algebra (A equation,※See Full-text). If B and H are finite algebra and Hopf algebra, respectively, then the linear dual (※See Full-text) is also a Hopf algebra. We show that the weak coaction admissible mapping system characterizes the new Hopf algebras (※See Full-text).

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.221-238
• /
• 2011

We prove the Hyers-Ulam stability of generalized Jensen's equations in Banach modules over a unital $C^{\ast}$-algebra. It is applied to show the stability of generalized Jensen's equations in a Hilbert module over a unital $C^{\ast}$-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital $C^{\ast}$-algebra.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.1105-1115
• /
• 2022

The main objective of this paper is to introduce the notion of AMR-algebra and its generalization, and to compare them with other algebras such as BCK, BCI, BCH, · · ·, etc. We show moreover that the K-part of AMR-algebra is an abelian group, and the weak AMR-algebra is also an abelian group and generalizes many known algebras like BCI, BCH, and G.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.363-368
• /
• 2010

In this paper we construct a subalgebra $L_8$ of $M_8({\mathbb{R}})$ which is a generalization of the algebra of quaternions. Moreover we prove that the algebra $L_8$ is the real Clifford algebra $Cl_3$, and so $L_8$ is a matrix representation of Clifford algebra $Cl_3$.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.51-62
• /
• 2002

The present paper gives a new construction of a quotient BCI(BCK)-algebra X/${\mu}$ by a fuzzy ideal ${\mu}$ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if ${\mu}$ is a fuzzy ideal (closed fuzzy ideal) of X, then X/${\mu}$ is a commutative (resp. positive implicative, implicative) BCK(BCI)-algebra if and only if It is a fuzzy commutative (resp. positive implicative, implicative) ideal of X Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra of X We show that if the period of every element in a BCI-algebra X is finite, then any fuzzy ideal of X is closed. Especiatly, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.

• Korean Journal of Mathematics
• /
• v.7 no.1
• /
• pp.103-110
• /
• 1999

For a group action ${\alpha}$ on a Kac algebra $\mathbb{K}$ with the crossed product Kac algebra $\mathbb{K}{\rtimes}_{\alpha}G$, we will show that ${\pi}_{\alpha}(\mathbb{K})$ is a sub-Kac algebra of $\mathbb{K}{\rtimes}_{\alpha}G$. We will also investigate the intrinsic group $G(\mathbb{K})$ of $\mathbb{K}$ and get a group action ${\beta}$ on a symmetric Kac algebra $\mathbb{K}_s(G(\mathbb{K})$ with the crossed product sub-Kac algebra $\mathbb{K}_s(G(\mathbb{K}){\rtimes}_{\beta}G$ of $\mathbb{K}{\rtimes}_{\alpha}G$.

• Journal of the Chungcheong Mathematical Society
• /
• v.11 no.1
• /
• pp.151-161
• /
• 1998

The odd spherical non-commutative tori $\mathbb{S}_{\omega}$ were defined in [2]. Assume that no non-trivial matrix algebra can be factored out of $\mathbb{S}_{\omega}$, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra $M_{km}(\mathbb{C})$. It is shown that the tensor product of $\mathbb{S}_{\omega}$ with the even Cuntz algebra $\mathcal{O}_{2d}$ has the trivial bundle structure if and, only if km and 2d - 1 are relatively prime, and that the tensor product of $\mathbb{S}_{\omega}$ with the generalized Cuntz algebra $\mathcal{O}_{\infty}$ has a non-trivial bundle structure when km > 1.

• Kyungpook Mathematical Journal
• /
• v.48 no.4
• /
• pp.529-543
• /
• 2008

It is shown that every almost linear mapping h : $A{\rightarrow}B$ of a unital PoissonC*-algebra A to a unital Poisson C*-algebra B is a Poisson C*-algebra homomorph when $h(2^nuy)\;=\;h(2^nu)h(y)$ or $h(3^nuy)\;=\;h(3^nu)h(y)$ for all $y\;\in\;A$, all unitary elements $u\;\in\;A$ and n = 0, 1, 2,$\codts$, and that every almost linear almost multiplicative mapping h : $A{\rightarrow}B$ is a Poisson C*-algebra homomorphism when h(2x) = 2h(x) or h(3x) = 3h(x for all $x\;\in\;A$. Here the numbers 2, 3 depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings. We prove the Cauchy-Rassias stability of Poisson C*-algebra homomorphisms in unital Poisson C*-algebras, and of homomorphisms in Poisson Banach modules over a unital Poisson C*-algebra.