• East Asian mathematical journal
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• 제23권1호
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• pp.75-82
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• 2007

In this paper we give a concrete computational method to characterize $S_3$-algebras.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.317-325
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• 2022

The concept of hom-set in an implicative algebra as an implicative algebra is introduced. The idea of sub implicative algebra in hom-set, 1-commutative algebra of hom-set are investigated. Different characterization theorems are proved.

• Journal of the Korean Mathematical Society
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• 제38권4호
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• pp.763-780
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• 2001

The use and development of of computer technology by algebraists over the last forty years has revolutionised the way in which algebraists think about algebra, and the way they teach it and conduct their research. This paper is a personal reflection on these changes by a somewhat unwilling computer user.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.207-212
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• 2024

In this paper, we study Malcev algebra bundles and Malcev algebra bundles of finite type. Lie algebra bundles and Lie transformation algebra bundles are defined using given Malcev algebra bundle and we conclude some results for finite type.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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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.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1105-1115
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• 2022

The main objective of this paper is to introduce the notion of AMR-algebra and its generalization, and to compare them with other algebras such as BCK, BCI, BCH, · · ·, etc. We show moreover that the K-part of AMR-algebra is an abelian group, and the weak AMR-algebra is also an abelian group and generalizes many known algebras like BCI, BCH, and G.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.633-645
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• 2023

In this paper, Completely V-Regular on semiring is defined and used to derive new theorems with some of its properties. This paper also illustrates V-Regular algebra and Completely V-Regular Algebra with examples and properties. By extending completely V-Regular to fuzzy, a new concept, fuzzy V-Regular is brought out and fuzzy completely V-Regular algebra is introduced too. It is also developed by defining the ideals of Completely V -Regular Algebra and fuzzy completely V-Regular algebra. Finally, this fuzzy algebra concept is applied in image processing to detect edges. This V-Regular Algebra is novel in the research area.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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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 Φ_F induced by a filter F and show that every congruence relation on a quasi-lattice implication algebra is a congruence relation Φ_F induced by a filter F.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.569-573
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• 2006

Nagata and Higman proved that any nil-algebra of finite nilindex is nilpotent of finite index. The Nagata-Higman Theorem can be formulated in terms of T-ideals. TheT-ideal generated by $a^n$ for all $a{\in}A$ is also generated by the symmetric polynomials. The symmetric polynomials play an importmant role in analyzing nil-algebra. We construct the incidence matrix with the symmetric polynomials. Using this incidence matrix, we determine the nilpotency index of nil-algebra of nil-index 3.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.343-361
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• 2004

We prove the generalized Hyers-Ulam-Rassias stability of cyclic functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with cyclic functional equations in Banach algebras.