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Gamaliel Cerda-Morales

Abstract

In this paper, we give quadratic approximation of generalized Tribonacci sequence {Vn}n ≥0 defined by Vn = rVn−1 + sV n−2 + tV n−3 (n ≥ 3) and use this result to give the matrix form of the n-th power of a companion matrix of {Vn}n ≥0. Then we re-prove the cubic identity or Cassini-type formula for {Vn} n ≥0 and the Binet’s formula of the generalized Tribonacci quaternions.

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Małgorzata Elżbieta Hryniewicka

Abstract

In the paper, we introduce the notion of a nondistributive ring N as a generalization of the notion of an associative ring with unit, in which the addition needs not be abelian and the distributive law is replaced by n0 = 0n = 0 for every element n of N. For a nondistributive ring N, we introduce the notion of a nondistributive ring of left quotients S −1 N with respect to a multiplicatively closed set SN, and determine necessary and sufficient conditions for the existence of S −1 N.

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M. Mast Zohouri

Abstract

Let (R, 𝔪) denote a commutative Noetherian local ring and let M be a finite R-module. In this paper, we study relative Cohen-Macaulay rings with respect to a proper ideal 𝔞 of R and give some results on such rings in relation with Artinianness, Non-Artinianness of local cohomology modules and Lyubeznik numbers. We also present some related examples to this issue.

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Aiyared Iampan

Abstract

In this paper, we introduce some new classes of algebras related to UP-algebras and semigroups, called a left UP-semigroup, a right UP-semigroup, a fully UP-semigroup, a left-left UP-semigroup, a right-left UP-semigroup, a left-right UP-semigroup, a right-right UP-semigroup, a fully-left UP-semigroup, a fully-right UP-semigroup, a left-fully UP-semigroup, a right-fully UP-semigroup, a fully-fully UP-semigroup, and find their examples.

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Akbar Paad

Abstract

In this paper, the concepts of n-fold implicative ideals and n-fold obstinate ideals in BL-algebras are introduced. With respect to this concepts, some related results are given. In particular, it is proved that an ideal is an n-fold implicative ideal if and only if is an n-fold Boolean ideal. Also, it is shown that a BL-algebra is an n-fold integral BL-algebra if and only if trivial ideal {0} is an n-fold obstinate ideal. Moreover, the relation between n-fold obstinate ideals and n-fold (integral) obstinate filters in BL-algebras are studied by using the set of complement elements. Finally, it is proved that ideal I of BL-algebra L is an n-fold obstinate ideal if and only if LT is an n-fold obstinate BL-algebra.

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Anil Khairnar and B.N. Waphare

Abstract

We prove that a p.q.-Baer *-ring forms a pseudo lattice with Conrad’s partial order and also characterize p.q.-Baer *-rings which are lattices. The initial segments of a p.q.-Baer *-ring with the Conrad’s partial order are shown to be an orthomodular posets.

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B. Ramoorthy Reddy and C. Jaya Subba Reddy

Abstract

The present paper shows some results on the commutativity of R: Let R be a prime ring and for any nonzero ideal I of R, if R admits a biderivation B such that it satisfies any one of the following properties (i) B([x, y], z) = [x, y], (ii) B([x, y], m) + [x, y] = 0, (iii) B(xoy, z) = xoy, (iv) B(xoy, z) + xoy = 0, (v) B(x, y)oB(y, z) = 0, (vi)B(x, y)oB(y, z) = xoz, (vii) B(x, y)oB(y, z) + xoy = 0, for all x, y, zR, then R is a commutative ring.

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Marapureddy Murali Krishna Rao and B. Venkateswarlu

Abstract

In this paper, as a further generalization of ideals, we introduce the notion of bi-interior ideal as a generalization of quasi ideal, bi-ideal and interior ideal of Γ-semiring and study the properties of bi-interior ideals of Γ-semiring. We prove that if M is a field Γ-semiring, then M is a bi-interior simple Γ-semiring.

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Cihat Abdioğlu, Ece Yetkin Çelikel and Angsuman Das

Abstract

In this paper we initiate the study of Armendariz graph of a commutative ring R and investigate the basic properties of this graph such as diameter, girth, domination number, etc. The Armendariz graph of a ring R, denoted by A(R), is an undirected graph with nonzero zero-divisors of R[x] (i.e., Z(R[x])*) as the vertex set, and two distinct vertices f(x)=i=0naixi and g(x)=j=0mbjxj are adjacent if and only if aibj = 0, for all i, j. It is shown that A(R), a subgraph of Γ(R[x]), the zero divisor graph of the polynomial ring R[x], have many graph properties in common with Γ(R[x]).

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Abdelaziz Amroune and Bouad Aissa

Abstract

The main goal of this paper is to investigate the aggregation of diverse families of binary fuzzy relations, fuzzy filters, and fuzzy lattices. Some links between these families and their images via an aggregation are explored.