• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1077-1095
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• 2015

In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of group extensions of the type of a crossed module and the one of equivariant group extensions.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1091-1097
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• 2009

In this paper, we investigate the extensions of generalized stable rings. It is shown that a ring R is a generalized stable ring if and only if R has a complete orthogonal set {e$_1$, . . . , e$_n$} of idempotents such that e$_1$Re$_1$, . . . , e$_n$Re$_n$ are generalized stable rings. Also, we prove that a ring R is a generalized stable ring if and only if R[[X]] is a generalized stable ring if and only if T(R,M) is a generalized stable ring.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.183-198
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• 2006

In this paper q-extensions of Genocchi numbers are defined and several properties of these numbers are presented. Properties of q-Genocchi numbers and polynomials are used to construct q-extensions of p-adic measures which yield to obtain p-adic interpolation functions for q-Genocchi numbers. As an application, general systems of congruences, including Kummer-type congruences for q-Genocchi numbers are proved.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.325-344
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• 2014

The aim of this paper is to generalize the theory of Hopf-Ore extension on Hopf algebras to Hopf group coalgebras. First the concept of Hopf-Ore extension of Hopf group coalgebra is introduced. Then we will give the necessary and sufficient condition for the Ore extensions to become a Hopf group coalgebra, and certain isomorphism between Ore extensions of Hopf group coalgebras are discussed.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.585-591
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• 2008

In 1981, Sen [4] have introduced the concept of $\Gamma$-semigroups. We have known that $\Gamma$-semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in $\Gamma$-semigroups and characterize the relationship between the extensions of ideals and some congruences in $\Gamma$-semigroups.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.25-35
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• 2013

In this paper, we introduce and study the concept of "strongly $t$-linked extensions", which is a stronger version of $t$-linked extensions of integral domains. We show that for an extension of Pr$\ddot{u}$fer $v$-multiplication domains, this concept is equivalent to that of "$w$-faithfully flat".

• Proceedings of the KACD Conference
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• 2003.05a
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• pp.289-289
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• 2003

I. Objectives Narrow long oval canals usually cannot be instrumented completely and uninstrumented extensions or irregularities usually remain. The aim of this study was to compare the ability of syringe irrigation and ultrasound irrigation to remove dentin debris from simulations of uninstrumented canal extensions and irregularities.(omitted)

• Journal of Integrative Natural Science
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• v.14 no.3
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• pp.139-146
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• 2021

The purpose of this paper is to classify the torsion-free extensions 1→ℤ³→𝛱→ℤ_𝜱→1 with injective abstract kernel 𝜙 : ℤ_𝜱→Aut(ℤ³). From this classification, we handle the sufficient conditions so as to classify the crystallographic groups of Sol⁴_m,n.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.443-454
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• 2021

In this paper, we discuss the backward extensions of Bergman shifts W_α(m), where $${\alpha}(m)\;:\;\sqrt{\frac{m}{m+1}},\;{\sqrt{\frac{m+1}{m+2}}},\;{\cdots},\;(m{\in}\mathbb{N})$$. We obtained a complete description of the n-hynonormality for backward one, two and three step extensions.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.68-77
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• 2021

This paper considers pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. We characterize pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. Moreover, we define pseudo derivations on the above stated Banach algebras and characterize this new notion on those algebras.