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Donglin Liu, Chunxiang Wang and Shaohui Wang

Abstract

The product graph Gm *Gp of two given graphs Gm and Gp, defined by J.C. Bermond et al.[J Combin Theory, Series B 36(1984) 32-48] in the context of the so-called (Δ,D)-problem, is one interesting model in the design of large reliable networks. This work deals with sufficient conditions that guarantee these product graphs to be hamiltonian-connected. Moreover, we state product graphs for which provide panconnectivity of interconnection networks modeled by a product of graphs with faulty elements.

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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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D. L. Kiran Kumar, H. G. Nagaraja and K. Venu

Abstract

In this paper we study the nature of Ricci solitons in D-homothetically deformed Kenmotsu manifolds. We prove that η-Einstein Kenmotsu metric as a Ricci soliton remains η-Einstein under D-homothetic deformation and the scalar curvature remains constant.

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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.