In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal,...

In this paper, with a new idea, we redefine generalized fuzzy ideal and investigate some of its properties. We generalize fuzzy prime ideals and introduce the notions of (∈,∈ ∨q)−fuzzy prime ideal of ordered semigroups. We characterize (∈,∈ ∨q)−fuzzy prime ideal by its image and level ideals. We establish necessary and sufficient condition for fuzzy set to be a (∈,∈ ∨q)−fuzzy prime ideal. 2010 ...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

Purpose The KneeAlign2 (KA2, OrthoAlign Inc.) accelerometer-based portable navigation system and patient-specific instrumentation (PSI; Signature, ZimmerBiomet) are widely used for ideal femoral component alignment in total knee arthroplasty (TKA). However, there has been no comparative study of the KA2 system, PSI, and conventional intramedullary instrumentation (CON). The purpose of this stud...

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

The concepts of a prime ideal of a distributively generated (d.g.) nearring R, a prime d.g. near-ring and an irreducible R-group are introduced1). The annihilating ideal of an irreducible R-group with an R-generator is a prime ideal. Consequently we define a prime ideal to be primitively prime if it is the annihilating ideal of such an R-group, and a d.g. near-ring to be a primitively prime nea...

Let O be an order in the number field K. When O 6= OK , O is Noetherian and onedimensional, but is not integrally closed, so it has at least one nonzero prime ideal that’s not invertible and O doesn’t have unique factorization of ideals. That is, some nonzero ideal in O does not have a unique prime ideal factorization. We are going to define a special ideal in O, called the conductor, that is c...

In this paper, we initiate the study of prime bi-ideals (fuzzy bi-ideals) in semirings. We define strongly prime, prime, semiprime, irreducible and strongly irreducible bi-ideals in semirings. We also define strongly prime, semiprime, irreducible, strongly irreducible fuzzy bi-ideals of semirings. We characterize those semirings in which each bi-ideal (fuzzy bi-ideal) is prime (strongly prime).

A private set intersection (PSI) protocol allows players to obtain the intersection of their inputs. While in its unilateral version only the client can obtain the intersection, the mutual PSI protocol enables all players to get the desired result. In this work, we construct a mutual PSI protocol that is significantly more efficient than the stateof-the-art in the computation overhead. To the b...

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.