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Abstract

In this note we study the analytic continuation of the Apostol-Vu multiple Fibonacci zeta functions

ζAVF,k(s1,,sk,sk+1)=1m1<<mk1Fm1s1Fm2s2FmkskFm1+m2++mksk+1,
where s 1, . . ., sk +1 are complex variables and Fn is the n-th Fibonacci number. We find a complete list of poles and their corresponding residues.

Abstract

This note is written to show that the definition of the LA- Γ -hypersemi-group and the definition of the ordered LA- Γ -hypersemigroup in [2] should be corrected and that it is not enough to replace the “Γ” of the ordered LA-Γ-semigroup by “◦ Γ ◦” to pass from an ordered LA- Γ -semigroup to an ordered LA- Γ -hypersemigroup. The definition of the (m,n)- Γ -hyperideal and the strange symbols used throughout the paper have no sense as well.

Abstract

We provide some properties of maximal Bp-subalgebras of B-algebras. In particular, we show that for each prime p, a finite B-algebra has a maximal Bp-subalgebra. We also show that for a finite B-algebra of order p r m, where (p, m) = 1, any two maximal Bp-subalgebras are conjugate and the number of maximal Bp-subalgebras is kp + 1 for some k ∈ 𝕑+.

Abstract

The main purpose of this paper is to provide an effective content of theory of ternary semigroups with involution by applying soft set theory concepts. In this paper, we introduce some basic terms and definitions of different ideals in ternary semigroups with involution. Further, we define soft ideals and soft filters in ternary semigroups with involution, and show how a soft set effects on a ternary semigroup with involution with the help of intersection and insertion of sets. We explore some properties using involution theoretic concepts in ternary semigroups for soft ideals and soft filters.

Abstract

Let 𝒭 be a ring with center Z(𝒭). A mapping f : 𝒭 → 𝒭 is said to be strong commutativity preserving (SCP) on 𝒭 if [f (x), f (y)] = [x, y] and is said to be strong anti-commutativity preserving (SACP) on 𝒭 if f (x) ◦ f (y) = xy for all x, y ∈𝒭. In the present paper, we apply the standard theory of differential identities to characterize SCP and SACP derivations of prime and semiprime rings.

Abstract

In this paper, the concept of quasi pseudo-complementation on an Almost Distributive Lattice (ADL) as a generalization of pseudo-complementation on an ADL is introduced and its properties are studied. Necessary and su cient conditions for a quasi pseudo-complemented ADL(q-p-ADL) to be a pseudo-complemented ADL(p-ADL) and Stone ADL are derived and the set S(L) = {a* | a ∈ L} is proved to be a Boolean algebra. Also, the notions of ∗−congruence and kernel ideals are introduced in a quasi-p-ADL and characterized kernel ideals. Finally, some equivalent conditions are given for every ideal of a quasi-p-ADL to be a kernel ideal.

Abstract

Let (P, ≤) be a poset with the least element 0. The intersection graph of ideals of P, denoted by G(P), is a graph whose vertices are all nontrivial ideals of P and two distinct vertices I and J are adjacent if and only if IJ ≠ {0}. In this paper, we study the planarity and outerplanarity of the intersection graph G(P). Also, we determine all posets with split intersection graphs.

Abstract

In this paper, we generalize the notion of principal ideal (resp. filter) on a lattice to the setting of intuitionistic fuzzy sets and investigate their various characterizations and properties. More specifically, we show that any principal intuitionistic fuzzy ideal (resp. filter) coincides with an intuitionistic fuzzy down-set (resp. up-set) generated by an intuitionistic fuzzy singleton. Afterwards, for a given intuitionistic fuzzy set, we introduce two intuitionistic fuzzy sets: its intuitionistic fuzzy down-set and up-set, and we investigate their interesting properties.

Abstract

The notion of a RM algebra, introduced recently, is a generalization of many other algebras of logic. The class of RM algebras contains (weak-)BCC algebras, BCH algebras, BCI algebras, BCK algebras and many others. A RM algebra is an algebra A = (A; →, 1) of type (2, 0) satisfying the identities: xx = 1 and 1 → x = x. In this paper we study the set of maximal elements of a RM algebra, branches of a RM algebra and moreover translation deductive systems of a RM algebra giving so called the Representation Theorem for RM algebras.

Abstract

Let D be a domain. By [4], D has “property SP” if every ideal of D is a product of radical ideals. It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals. In their article [4] Vaughan and Yeagy prove that a domain having property SP is an almost Dedekind domain. We give a very short and easy proof of this result.