Parween Ali Hummadi

• Doctor of Philosophy
• Salahaddin University-Erbil

Let Κ be a proper ideal of a commutative ring S. Then Κ is a strongly irreducible (SI) ideal if for any two ideals C and D of S, C∩D⊆ Κ implies C ⊆ Κ or D ⊆ Κ. We say a ring is strongly irreducible (SI) if all its ideals are strongly irreducible. In this paper some properties of such ring are given. The relations between SI rings and some types of...

In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the n-maximal ideal, the maximal dimension of a ring S (M. dim(S)), the maximal depth of an ideal K of S (M.d(K)) and maximal height of an ideal K(M.d(K)).

In this paper, the concepts of -sequence prime ideal and -sequence quasi prime ideal are introduced. Some properties of such ideals are investigated. The relations between -sequence prime ideal and each of primary ideal, -prime ideal, quasi prime ideal, strongly irreducible ideal, and closed ideal, are studied. Also, the ideals of a principal ideal...

In this paper we study semiunit elements in the group ring , where G is a cyclic group and we introduce and discuss strongly semiunit elements in , for , where p is an odd prime. We define and study tri-regular elements in and in the group ring , where G is a cyclic group.

this research was my MSc thesis with my supervisor Parween Ali hummadi

In this paper, we study Smarandache zero divisors, in Zn and the group ring Z2 G, for a cyclic group G of order 2n, we also study power joined elements and triple identity rings.

In this paper, we study some Smarandache (S) notions in some types of rings. Conditions are given under which is a Smarandache ring. We study Smarandache ideals, Smarandache subrings and Smarandache weakly Boolean rings. We discuss some types of Smarandache elements in rings. Moreover, we get some other results.

In this paper, we study Smarandache (S) specialdefinite rings and Smarandache (S)specialdefinite fields. We givecharacterizations of a S-special definite ringanda S-special definite field and determine some properties of each of them and obtain some result.

In this paper we study S-idempotents of the group ring \mathbb{Z}_2G where G is a finite cyclic group of order n. We give a condition on n such that every nonzero idempotent element of the group ring \mathbb{Z}_2G is Smarandache idempotent and we find Smarandache idempotents of the group ring KG, where K is an algebraically closed field of characte...

In this paper, we study Smarandache special definite groups. We give necessary and sufficient conditions for a group to be Smarandache special definite group(S-special definite group). Moreover we study Smarandache special definite subgroups, Smarandache special definite maximal ideals, Smarandache special definite minmal ideals.

Given a nonempty set X and a function f : X 6X, three pseudo-metrizable spaces are introduced. Some properties of these spaces and relations among them are studied and discussed.

In this paper we study S-idempotents of the group ring Z2G where G is a finite cyclic group of order . We give a condition on such that every nonzero idempotent element of the group ring Z2G is Smarandache idempotent and we find Smarandache idempotents of the group ring KG where K is an algebraically closed field of characteristic 0 and is a finite...

Let R be a commutative ring with identity. It is well known that a topology was defined for Spec(R)={I|IisaprimeidealofR} called the Zariski topology (prime spectrum). We generalize this idea for primary ideals. If P_Spec(R)={I|IisaprimaryidealofR}, we show that if R is a Principal Ideal Domain, then P_Spec(R) can be endowed with a topology similar...