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Initial fuzzy soft closure structures
Ali N. Koam,Ismail Ibedou,S. E. Abbas 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.17 No.2
In this paper, we introduce the notions of fuzzy soft interior spaces and fuzzy soft closure spaces. In particular, we prove the existence of initial fuzzy soft interior structures and initial fuzzy soft closure structures. From this fact, the category FSC is a topological category over SET.
Ali N.A. Koam,Azeem Haider,Moin A. Ansari 강원경기수학회 2019 한국수학논문집 Vol.27 No.1
In this paper we have introduced the concept of pseudo-metric which we induced from a pseudo-valuation on KU-algebras and investigated the relationship between pseudo-valuations and ideals of KU-algebras. Conditions for a real-valued function to be a pseudo-valuation on KU-algebras are provided.
ON STRONGLY 1-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS
Almahdi, Fuad Ali Ahmed,Bouba, El Mehdi,Koam, Ali N.A. Korean Mathematical Society 2020 대한수학회보 Vol.57 No.5
Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce a subclass of the class of 1-absorbing primary ideals called the class of strongly 1-absorbing primary ideals. A proper ideal I of R is called strongly 1-absorbing primary if whenever nonunit elements a, b, c ∈ R and abc ∈ I, then ab ∈ I or c ∈ ${\sqrt{0}}$. Firstly, we investigate basic properties of strongly 1-absorbing primary ideals. Hence, we use strongly 1-absorbing primary ideals to characterize rings with exactly one prime ideal (the UN-rings) and local rings with exactly one non maximal prime ideal. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the prime ideals, the primary ideals and the 1-absorbing primary ideals. In the end of this paper, we give an idea about some strongly 1-absorbing primary ideals of the quotient rings, the polynomial rings, and the power series rings.
On KU-Algebras containing (α, β)-US soft sets
Moin A. Ansari,Ali N.A. Koam,Azeem Haider 강원경기수학회 2020 한국수학논문집 Vol.28 No.1
In this paper, we connect $(\alpha, \beta)$ union soft sets and their ideal related properties with $KU$-algebras. In particular, we will study $(\alpha, \beta)$-union soft sets, $(\alpha, \beta)$-union soft ideals, $(\alpha, \beta)$-union soft commutative ideals and ideal relations in $KU$-algebras. Finally, a characterization of ideals in $KU$-algebras in terms of $(\alpha, \beta)$-union soft sets have been provided.