• Title, Summary, Keyword: computational algebra

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MIRROR d-ALGEBRAS

  • So, Keum Sook;Kim, Young Hee
    • Journal of applied mathematics & informatics
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    • v.31 no.3_4
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    • pp.559-564
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    • 2013
  • In this paper we investigate necessary conditions for the mirror algebra $(M(X),{\bigoplus},(0,0))$ to be a $d$-algebra (having the condition (D5), resp.) when (X, *, 0) is a d-algebra (having the condition (D5), resp.). Moreover, we obtain the necessary conditions for M(X) of a $d^*$-algebra X to be a $d^*$-algebra.

ON QUASI-LATTICE IMPLICATION ALGEBRAS

  • YON, YONG HO
    • Journal of applied mathematics & informatics
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    • v.33 no.5_6
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    • pp.739-748
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    • 2015
  • The notion of quasi-lattice implication algebras is a generalization of lattice implication algebras. In this paper, we give an optimized definition of quasi-lattice implication algebra and show that this algebra is a distributive lattice and that this algebra is a lattice implication algebra. Also, we define a congruence relation ΦF induced by a filter F and show that every congruence relation on a quasi-lattice implication algebra is a congruence relation ΦF induced by a filter F.

PRIME FILTERS OF COMMUTATIVE BE-ALGEBRAS

  • RAO, M. SAMBASIVA
    • 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.

A CAUCHY-JENSEN FUNCTIONAL INEQUALITY IN BANACH MODULES OVER A $C^*$-ALGEBRA

  • Najati, Abbas
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.233-241
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    • 2010
  • In this paper, we investigate the following functional inequality $${\parallel}f(\frac{x\;+\;y}{2}\;+\;z)\;+\;f(\frac{x\;+\;y}{2}\;+\;y)\;+\;f(\frac{y\;+\;z}{2}\;+\;x){\parallel\;\leq\;\parallel}2f(x\;+\;y\;+\;z)\parallel$$ in Banach modules over a $C^*$-algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a $C^*$-algebra.

FILTERS OF BE-ALGEBRAS WITH RESPECT TO A CONGRUENCE

  • RAO, M. SAMBASIVA
    • Journal of applied mathematics & informatics
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    • v.34 no.1_2
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    • pp.1-7
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    • 2016
  • Some properties of filters are studied with respect to a congru-ence of BE-algebras. The notion of θ-filters is introduced and these classes of filters are then characterized in terms of congruence classes. A bijection is obtained between the set of all θ-filters of a BE-algebra and the set of all filters of the respective BE-algebra of congruences classes.

PREGROUPS AND PRE-B-ALGEBRAS

  • WU, GANG;KIM, YOUNG HEE
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.51-57
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    • 2018
  • In this paper, we introduce the notions of pregroups, post-groups and pre-B-algebras, and we investigate their relations. Using this notions we give another proof that the notion of B-algebras coincides with the notion of pregroups.