• Title/Summary/Keyword: semi-homomorphism

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SEMI-HOMOMORPHISMS OF BCK-ALGEBRAS

  • Lee, Kyoung Ja;Jun, Young Bae
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.2
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    • pp.131-139
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    • 2009
  • As a generalization of a homomorphism of BCK-algebras, the notion of a semi-homomorphism of BCK-algebras is introduced, and its characterization is given. A condition for a semi-homomorphism to be a homomorphism is provided.

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CONTINUITY OF JORDAN *-HOMOMORPHISMS OF BANACH *-ALGEBRAS

  • Draghia, Dumitru D.
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.187-191
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    • 1993
  • In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

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CONTINUITY OF HOMOMORPHISMS AND DERIVATIONS ON BANACH ALGEBRAS

  • Park, Sung-Wook
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.109-115
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    • 1993
  • In 1940 Eidelheit showed that every homomorphism of a Banach algebra onto the Banach algebra B(X) of all bounded linear operators on a Banach space X is continuous. At about the same time, Gelfand proved that every homomorphism of a commutative Banach algebra into a commutative semi-simple Banach algebra is continuous. In [7] Johnson proved that every homomorphism of a Banach algebra onto non-commutative semi-simple Banach algebra is continuous, and this is still the most important result of this type. In this paper we are concerned with continuity of derivations on commutative Banach algebras and of homomorphisms into commutative Banach algebras. Throughout this paper we suppose that A is a commutative Banach algebra. R will denote the redical of A.

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CONTINUITY OF HOMOMORPHISMS BETWEEN BANACH ALGEBRAS

  • Cho, Tae-Geun
    • Bulletin of the Korean Mathematical Society
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    • v.20 no.2
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    • pp.71-74
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    • 1983
  • The problems of the continuity of homomorphisms between Banach algebras have been studied widely for the last two decades to obtain various fruitful results, yet it is far from characterizing the calss of Banach algebras for which each homomorphism from a member of the class into a Banach algebra is conitnuous. For commutative Banach algebras A and B a simple proof shows that every homomorphism .theta. from A into B is continuous provided that B is semi-simple, however, with a non semi-simple Banach algebra B examples of discontinuous homomorphisms from C(K) into B have been constructed by Dales [6] and Esterle [7]. For non commutative Banach algebras the problems of automatic continuity of homomorphisms seem to be much more difficult. Many positive results and open questions related to this subject may be found in [1], [3], [5] and [8], in particular most recent development can be found in the Lecture Note which contains [1]. It is well-known that a$^{*}$-isomorphism from a $C^{*}$-algebra into another $C^{*}$-algebra is an isometry, and an isomorphism of a Banach algebra into a $C^{*}$-algebra with self-adjoint range is continuous. But a$^{*}$-isomorphism from a $C^{*}$-algebra into an involutive Banach algebra is norm increasing [9], and one can not expect each of such isomorphisms to be continuous. In this note we discuss an isomorphism from a commutative $C^{*}$-algebra into a commutative Banach algebra with dense range via separating space. It is shown that such an isomorphism .theta. : A.rarw.B is conitnuous and maps A onto B is B is semi-simple, discontinuous if B is not semi-simple.

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ABSTRACT RELATIVE FOURIER TRANSFORMS OVER CANONICAL HOMOGENEOUS SPACES OF SEMI-DIRECT PRODUCT GROUPS WITH ABELIAN NORMAL FACTOR

  • Farashahi, Arash Ghaani
    • Journal of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.117-139
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    • 2017
  • This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

ON STRONGLY CONNECTED MODULES WITH PERFECT

  • PARK CHIN HONG;LEE JEONG KEUN;SHIM HONG TAE
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.653-662
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    • 2005
  • In this paper we shall give the relationships among $T_R,\;End_{R}(M),\;SEnd_{R}(M)\;and\;SAut_R(M)$ when M is a perfect R-module. If M and N are perfect modules, we get $SAut_{R}(M {\times}N){\cong}SAut_{R}(M){\times}SAut_R(N)$. Also we shall discuss that $_x(M)_H$ is a subgroup of $_x(M)$ if M is quasi-perfect and $_x(M)_H$ is a normal subgroup of $_x(M)$ if M is perfect.

On XML Data Processing through Implementing A Deductive and Object-oriented Database Language (연역 객체 지향 데이터베이스 언어 구현을 통한 XML 데이터 처리에 관한 연구)

  • Kim, Seong-Gyu
    • The KIPS Transactions:PartD
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    • v.9D no.6
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    • pp.991-998
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    • 2002
  • With the advent of XML and database languages armed with the object-oriented concept and deductive logic, the problem of efficient query processing for them has become a major issue. We describe a way of processing semi-structured XML data through an implementation of a Deductive and Object-oriented Database (DOODB) language with the explanation of query processing. We have shown how to convert an XML data model to a DOODB data model. We have then presented an efficient query processing method based on Connection Graph Resolution. We also present a knowledge-based query processing method that uses the homomorphism of objects in the database and the associative rule of substitutions.

A Queriable XML Compression using Inferred Data Types (추론한 데이타 타입을 이용한 질의 가능 XML 압축)

  • ;;Chung Chin-Wan
    • Journal of KIISE:Databases
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    • v.32 no.4
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    • pp.441-451
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    • 2005
  • HTML is mostly stored in native file systems instead of specialized repositories such as a database. Like HTML, XML, the standard for the exchange and the representation of data in the Internet, is mostly resident on native file systems. However. since XML data is irregular and verbose, the disk space and the network bandwidth are wasted compared to those of regularly structured data. To overcome this inefficiency of XML data, the research on the compression of XML data has been conducted. Among recently proposed XML compression techniques, some techniques do not support querying compressed data, while other techniques which support querying compressed data blindly encode data values using predefined encoding methods without considering the types of data values which necessitates partial decompression for processing range queries. As a result, the query performance on compressed XML data is degraded. Thus, this research proposes an XML compression technique which supports direct and efficient evaluations of queries on compressed XML data. This XML compression technique adopts an encoding method, called dictionary encoding, to encode each tag of XML data and applies proper encoding methods for encoding data values according to the inferred types of data values. Also, through the implementation and the performance evaluation of the XML compression technique proposed in this research, it is shown that the implemented XML compressor efficiently compresses real-life XML data lets and achieves significant improvements on query performance for compressed XML data.