In this paper, we introduce the notions of intuitionistic fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each intuitionistic fuzzy bi-ideal is semiprime and strongly prime. Key words: Intuitionistic fuzzy set; intuitionistic fuzzy bi-ideal; intuitionistic fuzzy prime (resp. strongly prime and semiprime) ...

We study (and sometimes introduce) the notions generic stability, regularity, homogeneous pregeometries, quasiminimality, and their mutual relations, in arbitrary first order theories. We prove that “infinite-dimensional homogeneous pregeometries” coincide with generically stable strongly regular types (p(x), x = x). We prove that in a theory without the strict order property, regular types are...

In this paper, we determine two families R and G of subsets of a hyperring R and sufficient conditions such that two geometric spaces (R,R) and (R,G) are strongly transitive. Moreover, we prove that the relations Γ and α are strongly regular equivalence relations on a hyperfield or a hyperring such that (R,+) has an identity element.

in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

Let Γ be a distance-regular graph with diameter d and Kneser graph K = Γd, the distance-d graph of Γ. We say that Γ is partially antipodal when K has fewer distinct eigenvalues than Γ. In particular, this is the case of antipodal distance-regular graphs (K with only two distinct eigenvalues), and the so-called half-antipodal distance-regular graphs (K with only one negative eigenvalue). We prov...

Inspired by some intriguing examples, we study uniform association schemes and uniform coherent configurations. Perhaps the most important subclass of these objects is the class of cometric Q-antipodal association schemes. The concept of a cometric association scheme (the dual version of a distance-regular graph) is well-known; however, until recently it has not been studied well outside the ar...

We study a generalization of strongly regular graphs. We call a graph strongly walkregular if there is an ` > 1 such that the number of walks of length ` from a vertex to another vertex depends only on whether the two vertices are the same, adjacent, or not adjacent. We will show that a strongly walk-regular graph must be an empty graph, a complete graph, a strongly regular graph, a disjoint un...

Let $R$ be an associative ring with identity. An element $x in R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if there exist $g in G$, $n in mathbb{Z}$ and $r in R$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). A ring $R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if every element of $R$ is $mathbb{Z}G$-regular (resp. strongly $...

‎in this paper‎, ‎the type-{rm ii} matrices on (negative) latin square graphs are considered and it is proved that‎, ‎under‎ ‎certain conditions‎, ‎the nomura algebras of such type-{rm ii} matrices are trivial‎. ‎in addition‎, ‎we construct type-{rm ii} matrices‎ ‎on doubly regular tournaments and show that the nomura algebras of such matrices are also trivial‎.