Let [Formula: see text] be a commutative ring with identity. The co-maximal ideal graph of text], denoted by is simple whose vertices are proper ideals which not contained in the Jacobson radical and two distinct adjacent if only text]. In this paper, we use Gallai’s Theorem concept strong resolving to compute metric dimension for graphs rings. Explicit formulae dimension, depending on whether ...

In this paper, basing our consideration on the sets with the apartness relation, we analyze characteristics of some special relations to these sets such as co-order and co-quasiorder and coequality relations. In addition, we analyze two special classes of subsets, co-filters and co-ideals, of ordered set under a co-quasiorder relation. This investigation is into the Bishop’s Constructive mathem...

Let R be a Noetherian commutative ring containing a eld. The test ideal, introduced by Hochster and Huneke in HH1], has emerged as an important object associated to R. The test ideal can be deened as the largest ideal J of R such that JI I for all ideals I of R where I denotes the tight closure of I. Although it is not obvious that a ring R admits a non-zero test ideal, Hochster and Huneke show...

Lattice-theoretic ideals have been used to define and generate non granular rough approximations over general approximation spaces over the last few years by few authors. The goal of these studies, in relation based rough sets, have been to obtain nice properties comparable to those of classical rough approximations. In this research paper, these ideas are generalized in a severe way by the pre...

In this note first we define the notions of fuzzy positive implicativehyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems whichcharacterize the above notions according to the level subsets. Also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperBCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7and 8. Then, we define the no...

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.

This paper presents a criterion for testing the irreducibility of a polynomial over an algebraic extension field. Using this criterion and the characteristic set method, the authors give a criterion for testing whether certain difference ascending chains are strong irreducible, and as a consequence, whether the saturation ideals of these ascending chains are prime ideals.