• Korean Journal of Mathematics
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• v.31 no.4
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• pp.465-477
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• 2023

In this paper, the concepts of soft PMS-algebras, soft PMS-subalgebras, soft PMS-ideals, and idealistic soft PMS-algebras are introduced, and their properties are studied. The restricted intersection, the extended intersection, union, AND operation, and the cartesian product of soft PMS-algebras, soft PMS-subalgebras, soft PMS-ideals, and idealistic soft PMS-algebras are established. Moreover, the homomorphic image and homomorphic pre-image of soft PMS-algebras are also studied.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.685-692
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• 2000

We introduce the notion of T-fuzzy circled subalgebras, and obtain some related results.

• East Asian mathematical journal
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• v.21 no.1
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• pp.9-19
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• 2005

In this paper, some properties of intuitionistic fuzzy o-subalgebras of BCK-algebra with condition(S) are investigated.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.451-457
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• 2002

Let (R, m, k) be a maximal commutative k-subalgebra of M$\sub$n/(k) where the index of nilpotency i(m) of m is 3. If the socle of R is of special case, then we can construct some isomorphic maximal commutative subalgebras.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.291-299
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• 1999

Let ${\Omega}$ be the set of all commutative $k$-subalgebras of 14 by 14 matrices over a field $k$ whose dimension is 13 and index of Jacobson radical is 3. Then we will find the equivalent condition for a commutative subalgebra to be maximal.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.403-410
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• 2007

Using the belongs to relation (${\in}$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${\alpha}$, ${\beta}$)-fuzzy subalgebras where ${\alpha}$ and ${\beta}$ areany two of {${\in}$, q, ${\in}{\vee}q$, ${\in}{\wedge}q$} with ${\alpha}{\neq}{\in}{\wedge}q$ was already introduced, and related properties were investigated (see [3]). In this paper, we give a condition for an (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra to be an (${\in}$, ${\in}$)-fuzzy subalgebra. We provide characterizations of an (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra. We show that a proper (${\in}$, ${\in}$)-fuzzy subalgebra $\mathfrak{A}$ of X with additional conditions can be expressed as the union of two proper non-equivalent (${\in}$, ${\in}$)-fuzzy subalgebras of X. We also prove that if $\mathfrak{A}$ is a proper (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra of a CK/BCI-algebra X such that #($\mathfrak{A}(x){\mid}\mathfrak{A}(x)$ < 0.5} ${\geq}2$, then there exist two prope non-equivalent (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebras of X such that $\mathfrak{A}$ can be expressed as the union of them.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.645-651
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• 2012

Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of N-subalgebras and N-ideals of X are introduced, and their relations/properties are investigated.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.261-272
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• 2001

The intuitionistic fuzzification of a subalgebra in a BCK/BCI-algebra is considered, and related results are investigated. The notion of equivalence relations on the family of all intuitionistic fuzzy subalgebras of a BCK/BCI-algebra is introduced, and then some properties are discussed.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.703-711
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• 2005

Using the belongs to relation ($\in$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${\alpha},\;{\beta}$)-fuzzy subalgebras where ${\alpha},\;{\beta}$ are any two of $\{\in,\;q,\;{\in}\;{\vee}\;q,\;{\in}\;{\wedge}\;q\}$ with $\;{\alpha}\;{\neq}\;{\in}\;{\wedge}\;q$ is introduced, and related properties are investigated.

• East Asian mathematical journal
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• v.21 no.1
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• pp.49-60
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• 2005

In this paper we introduced Semi-neutral BCK-algebra and investigate some of its properties. The notions of ideals and subalgebras coincide in Semi-neutral BCK-algebras. We also show that if the number of nonzero elements in a Semi-neutral BCK-algebra is n, then the number of ideals/subalgebras in it is $2^n$. Further, we solved an open problem posed by W.A. Dudek in [2].