• 충청수학회지
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• 제14권1호
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• pp.49-59
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• 2001

In this paper, we introduce an extended notion of regular homomorphism of minimal sets by considering a certain subgroup of the group of automorphisms of a universal minimal transfomation group.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.849-856
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• 2014

In this paper we introduce the notion of medial B-algebras, and we obtain a fundamental theorem of B-homomorphism for B-algebras.

• Korean Journal of Mathematics
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• 제18권1호
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• pp.79-86
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• 2010

In this paper we give some results on homomorphisms of flows. In particular, we investigate the sufficient conditions for the homomorphism of flows to be its own regularizer.

• 한국수학교육학회지시리즈A:수학교육
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• 제22권1호
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• pp.21-23
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• 1983

(1) Let f : XlongrightarrowX' be a homomorphism of BCK-algebras and let A,B be ideals of X and X' respectively such that f(A)⊂B. Then there is a unique homomorphism h : X/AlongrightarrowX'/B such that the diagram(equation omitted) commutes. (2) The class of all complexes of BCK-algebras becomes a category.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.273-278
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• 1997

Let A be a Banach algebra and B a semisimple annifilator Banach algebra. Then every homomorphism from A into B with range is continuous. Also we obtain condition s for the automatic continuity of homomorphism with dense range.

• East Asian mathematical journal
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• 제36권1호
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• pp.101-114
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• 2020

In this paper, we investigate commutativity of semiprime rings with a derivation which is strongly commutativity preserving and acts as a homomorphism or as an anti-homomorphism on a nonzero Lie ideal.

• 충청수학회지
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• 제11권1호
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• pp.59-71
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• 1998

In this paper we define a regular relation with respect to a homomorphism in transformation groups and we find the equivalent conditions for the relation to be an equivalence relation.

• 충청수학회지
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• 제21권4호
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• pp.555-562
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• 2008

In this paper, it will be given a necessary and sufficient condition for a function to be an r-homomorphism in connection with the subgroups of the automorphism group of a universal minimal set.

• 대한수학회논문집
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• 제33권1호
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• pp.165-170
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• 2018

In this paper, we show that every unital n-Jordan homomorphism ${\varphi}$ from a Banach algebra ${\mathcal{A}}$ onto a semisimple commutative Banach algebra B is continuous.

• 대한수학회지
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• 제43권2호
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.