• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.579-591
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• 2015

Properties of prime filters are studied in BE-algebras as well as in commutative BE-algebras. An equivalent condition is derived for a BE-algebra to become a totally ordered set. A condition L is introduced in a commutative BE-algebra in ordered to study some more properties of prime filters in commutative BE-algebras. A set of equivalent conditions is derived for a commutative BE-algebra to become a chain. Some topological properties of the space of all prime filters of BE-algebras are studied.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.483-494
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• 2012

In this paper we study properties of commutative BE-algebras and we give the construction of quotient (X/I; *, I) of a commutative BE-algebra X via an obstinate ideal I of X. We construct upper semilattice and prove that is a nearlattice. Finally we define and study commutative ideals in BE-algebras.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.233-242
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• 2012

The notions of terminal sections of $BE$-algebras are introduced. Characterizations of a commutative $BE$-algebra are provided.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1937-1956
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• 2013

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are introduced, and related properties and relations are investigated. Conditions for a union-soft ideal to be closed are provided. Conditions for a union-soft ideal to be a union-soft commutative ideal are also provided. Characterizations of (closed) union-soft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.

• 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.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.73-84
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• 2008

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to commutative ideals in BCK-algebras. The notion of an intuitionistic fuzzy commutative ideal of a BCK-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy commutative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy commutative ideal are given. Using a collection of commutative ideals, intuitionistic fuzzy commutative ideals are established.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.375-384
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• 2009

Characterizations of simulative WFI-algebras are provided. The notion of commutators, doubly simulative parts, doubly simulative WFI-algebras, and WFI-morphisms are introduced. Using the notion of commutators, the conditions for a WFI-algebra to be simulative are given. Characterizations of doubly simulative WFI-algebras are discussed. Using the notion of doubly simulative WFI-algebras, a commutative pomonoid is established.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.367-372
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• 1995

In 1955 Singer and Wermer [12] proved that every bounded derivation on a commutative Banach algebra maps into its radical. They conjectured that the continuity of the derivation in their theorm can be removed. In 1988 Thomas [13] proved their conjecture ; Every derivation on a commutative Banach algebra maps into its radical. For noncommutative versions, in 1984 B. Yood [15] proved that the continuous derivations on Banach algebras satisfing [D(a),b] $\in$ Rad(A) for all a, b $\in$ A have the radical range, where [a,b] will be denote the commutator ab-ba. In 1990 M.Bresar and J.Vukman [1] have generlized Yood's result, that is, the continuous linear Jordan derivation on Banach algebra that satisfies [D(a),a] $\in$ Rad(A) for all a $\in$ A has the radical range. In next year Mathieu and Murphy [5] proved that every bounded centralizing derivation on Banach algebras has its image in the radical. Mathieu and Runde [6] removed the boundedness of that.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.51-62
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• 2015

Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.

• Journal of the Chungcheong Mathematical Society
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• v.2 no.1
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• pp.37-44
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• 1989

In this paper, it is shown that automatic continuity of derivations on some semi prime Banach algebras can be extended to higher derivations. In particular, we show that if every prime ideal is closed in a commutative semi prime Banach algebra then every higher derivation on it is continuous.