Let L be a lattice, 𝒥(L) be the set of ideals of L and S be a subset of 𝒥 (L). In this paper, we introduce an undirected Cayley graph of L, denoted by ΓL,S with elements of 𝒥 (L) as the vertex set and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of S such that I ∨ K = J or J ∨ K = I. We study some basic properties of the graph ΓL,S such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of ΓL,S.
In this paper, we initiate the discourse on the properties that hold in an almost semi-Heyting algebra but not in an semi-Heyting almost distributive lattice. We establish an equivalent condition for an almost semi-Heyting algebra to become a Stone almost distributive lattice. Moreover a glance about dense elements in an almost semi-Heyting algebra followed by study of some algebraic properties on them. Finally, we perceive that the kernel of homomorphism is equal to the dense element set.
In this article, we introduce the notions of pseudosymmetric hyperideals and globally idempotent ternary semihypergroups and present various examples for them. We prove that if a ternary semihypergroup is globally idempotent, then every maximal hyperideal is a prime hyperideal. Also we study some properties of prime, completely prime and pseudosymmetric hyperideals of a ternary semihypergroup and characterize them. The interrelation among them is considered in ternary semihypergroups.
In this paper, we define and study the bivariate complex Fibonacci and Lucas polynomials. We introduce a operator in order to derive some new symmetric properties of bivariate complex Fibonacci and bivariate complex Lucas polynomials, and give the generating functions of the products of bivariate complex Fibonacci polynomials with Gaussian Fibonacci, Gaussian Lucas and Gaussian Jacobsthal numbers, Gaussian Pell numbers, Gaussian Pell Lucas numbers. By making use of the operator defined in this paper, we give some new generating functions of the products of bivariate complex Fibonacci polynomials with Gaussian Jacobsthal, Gaussian Jacobsthal Lucas polynomials and Gaussian Pell polynomials.
Directed graphs without multiple edges can be represented as algebras of type (2, 0), so-called graph algebras. A graph is said to satisfy an identity if the corresponding graph algebra does, and the set of all graphs satisfying a set of identities is called a graph variety. We describe the graph varieties axiomatized by certain groupoid identities (medial, semimedial, autodistributive, commutative, idempotent, unipotent, zeropotent, alternative).
In this paper we investigate some isomorphism theorems in EQ-algebras. After establishing some basic results we give the Fundamental Homomorphism Theorem and by using it we state and prove some other isomorphism theorems. We also state and prove a correspondence theorem. Next, using some results of the theory of universal algebra we characterize subdirectly irreducible EQ-algebras.