• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.307-315
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• 2007

We study crossed products of the free group and semigroup $C^*-algebras$ by actions of ${\mathbb{R}$, i.e., flows, and estimate and compute their stable rank.

• East Asian mathematical journal
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• v.15 no.2
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• pp.301-312
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• 1999

In this paper, we study the nonlinear ergodic retraction theorems for an asymptotically nonexpansive semigroup with nonconvex and nonclosed domains in Hilbert spaces.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.45-52
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• 1998

In this paper, we establish the exponential formula for C-semigroup. If A is the generator of a C-semigroup S(t), then S(t) can be represented by exp(tA) in some sense.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.639-641
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• 2004

We introduce the notion of closure $\Gamma$-semigroups. We give a condition for a closure $\Gamma$-semigroup to be $\Gamma$-central, and we show that the $\Gamma$-centralizer of a closure $\Gamma$-semigroup is a $\Gamma$-subsemigroup.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.627-635
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• 2018

In this paper, we use the notion of characters of transformations provided in [8] by Purisang and Rakbud to define a notion of weak regularity of transformations on an arbitrarily fixed set X. The regularity of a semigroup of weakly regular transformations on a set X is also investigated.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1577-1588
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• 2019

We show a multiple recurrence theorem for topological dynamical systems with countable directed partial semigroup actions, which generalizes the well-know IP-version of multiple recurrence theorem proved by Furstenberg and Weiss.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.133-146
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• 2021

For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.443-456
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• 2005

Let G be a Lie group, let L(G) be its Lie algebra, and let exp : $L(G){\rightarrow}G$ denote the exponential mapping. For $S{\subseteq}G$, we define the tangent set of S by $L(S)\;=\;\{X\;{\in}\;L(G)\;:\;exp(tX)\;\in\;S\;for\;all\;t\;{\geq}\;0\}$. We say that a semigroup S is strictly infinitesimally generated if S is the same as the semigroup generated by exp(L(S)). We find a tangent set of the semigroup of all non-singular totally positive matrices and show that the semigroup is strictly infinitesimally generated by the tangent set of the semigroup. This generalizes the familiar relationships between connected Lie subgroups of G and their Lie algebras

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.367-381
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• 2014

The notion of ${\Gamma}$-semigroups was introduced by Sen in 1981 and that of fuzzy sets by Zadeh in 1965. Any semigroup can be reduced to a ${\Gamma}$-semigroup but a ${\Gamma}$-semigroup does not necessarily reduce to a semigroup. In this paper, we study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in regular, left regular, right regular, intra-regular, semisimple ordered ${\Gamma}$-semigroups.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.9-13
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• 1983

M$_{n}$(F) denotes the set of all n*n matrices over F={0, 1}. For a, b.mem.F, define a+b=max{a, b} and ab=min{a, b}. Under these operations a+b and ab, M$_{n}$(F) forms a multiplicative semigroup (see [1], [4]) and we call it the semigroup of the n*n boolean matrices over F={0, 1}. Since the semigroup M$_{n}$(F) is the matrix representation of the semigroup B$_{n}$ of the binary relations on the set X with n elements, we may identify M$_{n}$(F) with B$_{n}$ for finding all D-classes.l D-classes.