Browsing by Author "Kurtulmaz, Yosum"
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Almost unitclean rings
Chen, H.; Köse, H.; Kurtulmaz, Yosum (Editura Academiei Romane, 2019)A ring R is almost unitclean provided that every element in R is equivalent to the sum of an idempotent and a regular element. We investigate conditions under which a ring is almost unitclean. We prove that every ring ... 
Duo property for rings by the quasinilpotent perspective
Harmancı, A.; Kurtulmaz, Yosum; Üngör, B. (Vasyl Stefanyk Precarpathian National University, 20210316)In this paper, we focus on the duo ring property via quasinilpotent elements, which gives anew kind of generalizations of commutativity. We call this kind of ringsqnilduo. Firstly, someproperties of quasinilpotents in a ... 
Local comparability of exchange ideals
Köse, H.; Kurtulmaz, Yosum; Chen, H. (Hacettepe University, 2019)An exchange ideal I of a ring R is locally comparable if for every regular x ∈ I there exists a right or left invertible u ∈ 1+I such that x = xux. We prove that every matrix extension of an exchange locally comparable ... 
A nil approach to symmetricity of rings
Üngör, B.; Köse, H.; Kurtulmaz, Yosum; Harmancı, A. (Allahabad Mathematical Society, 2018)We introduce a weakly symmetric ring which is a generalization of a symmetric ring and a strengthening of both a GWS ring and a weakly reversible ring, and investigate properties of the class of this kind of rings. A ring ... 
On πMorphic modules
Harmanci, A.; Kose, H.; Kurtulmaz, Yosum (Hacettepe University, Department of Mathematics, 2013)Let R be an arbitrary ring with identity and M be a right Rmodule with S = End(MR). Let f ∈ S. f is called πmorphic if M/f n(M) ∼=rM(fn) for some positive integer n. A module M is called πmorphic if every f ∈ S is ... 
Reflexivity of rings via nilpotent elements
Harmancı, A.; Köse, H.; Kurtulmaz, Yosum; Üngör, B. (Union Matematica Argentina, 2020)An ideal I of a ring R is called left Nreflexive if for any a ∈ nil(R) and b ∈ R, aRb ⊆ I implies bRa ⊆ I, where nil(R) is the set of all nilpotent elements of R. The ring R is called left Nreflexive if the zero ideal ... 
Rings having normality in terms of the Jacobson radical
Köse, H.; Kurtulmaz, Yosum; Harmancı, A. (Springer, 2020)A ring R is defined to be Jnormal if for any a,r∈Ra,r∈R and idempotent e∈Re∈R, ae=0ae=0 implies Rera⊆J(R)Rera⊆J(R), where J(R) is the Jacobson radical of R. The class of Jnormal rings lies between the classes of weakly ... 
Rings in which elements are a sum of a central and a unit element
Kurtulmaz, Yosum; Halıcıoğlu, S.; Harmancı, A.; Chen, H. (The Belgian Mathematical Society, 2019)In this paper we introduce a new class of rings whose elements are a sum of a central and a unit element, namely a ring RR is called CUCU if each element a∈Ra∈R has a decomposition a=c+ua=c+u where cc is central and uu is ... 
Semicommutativity of amalgamated rings
Köse, H.; Kurtulmaz, Yosum; Üngör, B.; Harmancı, A. (Journal of Mathematical Research with Applications, 2018)In this paper, we study some cases when an amalgamated construction A ◃▹f I of a ring A along an ideal I of a ring B with respect to a ring homomorphism f from A to B, is prime, semiprime, semicommutative, nilsemicommutative ... 
Structure theory of central simple ℤdgraded algebras
Koç, C.; Kurtulmaz, Yosum (TÜBİTAK, 2012)This paper investigates the structure theory of ℤd central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are ...