• Title, Summary, Keyword: transitive algebras

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FUZZY TRANSITIVE FILTERS OF BE-ALGEBRAS

  • Rao, M. Sambasiva
    • Journal of the Chungcheong Mathematical Society
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    • v.30 no.2
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    • pp.213-226
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    • 2017
  • The concept of fuzzy transitive filters is introduced in BE-algebras. Some sufficient conditions are established for every fuzzy filter of a BE-algebra to become a fuzzy transitive filter. Some properties of fuzzy transitive filters are studied with respect to fuzzy relations and cartesian products.

TRANSITIVE AND ABSORBENT FILTERS OF LATTICE IMPLICATION ALGEBRAS

  • Rao, M. Sambasiva
    • Journal of applied mathematics & informatics
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    • v.32 no.3_4
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    • pp.323-330
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    • 2014
  • The notion of transitive filters is introduced in lattice implication algebras. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. The concept of absorbent filters is introduced and their properties are studied. A set of equivalent conditions is obtained for a filter to become an absorbent filter.

ON GENERALIZED UPPER SETS IN BE-ALGEBRAS

  • Ahn, Sun-Shin;So, Keum-Sook
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.281-287
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    • 2009
  • In this paper, we develop the idea of a generalized upper set in a BE-algebra. Furthermore, these sets are considered in the context of transitive and self distributive BE-algebras and their ideals, providing characterizations of one type, the generalized upper sets, in terms of the other type, ideals.

AN APPLICATION OF COMPLICATEDNESS TO BH-ALGEBRAS

  • Kim, Eun-Mi;Ahn, Sun-Shin
    • The Pure and Applied Mathematics
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    • v.18 no.4
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    • pp.293-304
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    • 2011
  • The notions of an initial section and a special set in BH-algebras are defined and some of their properties are obtained. The notion of a complicated BH-algebra is introduced and some related properties are obtained. Finally, the notion of essences in BH-algebras are defined, and many properties are investigated.

SOME PROPERTIES OF DERIVATIONS ON CI-ALGEBRAS

  • Lee, Yong Hoon;Rhee, Min Surp
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.2
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    • pp.297-307
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    • 2014
  • The present paper gives the notion of a derivation on a CI-algebra X and investigates related properties. We define a set $Fix_d(X)$ by $Fix_d(X)=\{x{\in}X{\mid}d(x)=x\}$, where d is a derivation on a CI-algebra X. We show that $Fix_d(X)$ is a subalgebra of X. Also, we prove some one-to-one and onto derivation theorems. Moreover, we study a regular derivation on a CI-algebra and an isotone derivation on a transitive CI-algebra.

MULTIPLICITY-FREE ACTIONS OF THE ALTERNATING GROUPS

  • Balmaceda, Jose Maria P.
    • Journal of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.453-467
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    • 1997
  • A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

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