• The Pure and Applied Mathematics
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• v.28 no.3
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• pp.217-234
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• 2021

In this paper, first we introduce the new class of HV-BE-algebra as a generalization of a (hyper) BE-algebra and prove some basic results and present several examples. Then, we construct the HV-BE-algebra associated to a BE-algebra (namely BL-BE-algebra) based on "Begins lemma" and investigate it.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.407-419
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• 2009

The simple non-associative algebra $N(e^{A_S},q,n,t)_k$ and its simple sub-algebras are defined in the papers [1], [3], [4], [5], [6], [12]. We define the non-associative algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$ and its antisymmetrized algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$. We also prove that the algebras are simple in this work. There are various papers on finding all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [3], [5], [6], [9], [12], [14], [15]). We also find all the derivations $Der_{anti}(WN(e^{{\pm}x^r},0,2)_B^-)$ of te antisymmetrized algebra $WN(e^{{\pm}x^r}0,2)_B^-$ and every derivation of the algebra is outer in this paper.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.227-236
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• 2006

Several authors find all the derivations of an algebra [1], [3], [7]. A Weyl type non-associative algebra and its sub algebra are defined in the paper [2], [3], [10]. All the derivations of the non-associative algebra $\overline{WN_{0,0,s1}$ is found in this paper [4]. We find all the derivations of the non-associative algebra $\overline{WN_{0,s,01}$ in this paper [5].

• East Asian mathematical journal
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• v.23 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.401-410
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• 2002

We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's 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 generalized Jensen's functional equations in Banach algebras.

• East Asian mathematical journal
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• v.21 no.2
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• pp.171-181
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• 2005

In this paper we investigate some more properties of of $S_3$-algebras. We also prove that the class of $S_3$-algebras is contained in the class of commutative BCI-algebras.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.627-634
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• 2006

A Weyl type algebra is defined in the book ([4]). A Weyl type non-associative algebra $\={WP_{m,n,s}}$ and its restricted sub-algebra $\={WP_{m,n,s_{\gamma}}}$ are defined in various papers ([1], [12], [3], [11]). Several authors 0nd all the derivations of an associative (Lie or non-associative) algebra in the papers ([1], [2], [12], [4], [6], [11]). We find all the non-associative algebra derivations of the non-associative algebra $\={WP_{0,2,0_B}$, where $B=\{{\partial}_0,\;{\partial}_1,\;{\partial}_2,\;{\partial}_{12},\;{\partial}^2_1,\;{\partial}^2_2\}$.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.481-489
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• 2005

We first show that any complete MV-algebra whose Boolean subalgebra of idempotent elements is atomic, called a complete MV-algebra with atomic center, is isomorphic to a product of unit interval MV-algebra 1's and finite linearly ordered MV-algebras of A(m)-type $(m{\in}{\mathbb{Z}}^+)$. Secondly, for a semi-simple MV-algebra A, we introduce a completion ${\delta}(A)$ of A which is a complete, MV-algebra with atomic center. Under their intrinsic topologies $(see\;{\S}3)$ A is densely embedded into ${\delta}(A)$. Moreover, ${\delta}(A)$ has the extension universal property so that complete MV-algebras with atomic centers are epireflective in semi-simple MV-algebras

• Journal of applied mathematics & informatics
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• v.41 no.3
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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.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.237-248
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• 2023

The aim of this paper is to study the concept of s-topological d-algebras which is a d-algebra supplied with a certain type of topology that makes the binary operation defined on it d-topologically continuous. This concept is a generalization of the concept of topological d-algebra. We obtain several properties of s-topological d-algebras.