ON SOME PROPERTIES OF UU AND UJ RINGS

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dc.contributor.authorHantouli, Maisoon
dc.date.accessioned2025-05-08T10:42:40Z
dc.date.available2025-05-08T10:42:40Z
dc.date.issued2025-01-15
dc.description.abstractIn 2015, Grigore Calugareanu introduced and studied UU-rings as a new class of rings. He named a ring R by a UU-ring if each unit element x of R is of the form, x = 1 + n, for some t ∈ N il(R) (N il(R) denotes the set of nil-potent elements of R). He discussed some basic properties of these rings and provided some basic examples of UU and nonUU-rings. More properties and characterizations of UU-rings were provided by Peter Vassilev Danchev and Tsit-Yuen Lam in 2016. The first part of this thesis aims to reproduce and validate the work done in the literature about the UU-ring property, as well as discuss more properties of such rings. For example, in Chapter 2, we study the transfer of the UU-ring property in different ring extensions; such as the product of rings, the matrix ring, the polynomial ring, and the trivial ring extension. In 2017, M. Tamer Kosan, Andre Leroy, and Jerzy Matszuk investigated another new ring concept and called it UJ rings. They defined a ring R to be a UJ ring if each unit element x of R can be written in the form x = 1 + j, for some j ∈ J(R) (J(R) denotes the Jacobson-radical of R). It is well known that in the commutative case N il(R) ⊆ J(R) and so that the class of UU-rings is a subclass of the class of UJ rings. The second part of this thesis is devoted to studying the UJ ring property and discussing some of its relations with other ring concepts such as UU-rings, clean rings, and nil-clean rings, ..., also to determine the transfer of UJ property in the polynomial ring and its relation with Kothe’s problem.
dc.identifier.urihttps://hdl.handle.net/20.500.11888/20060
dc.language.isoen
dc.publisherAn-najah National University
dc.supervisorAdrbeh, Khlid
dc.titleON SOME PROPERTIES OF UU AND UJ RINGS
dc.title.alternativeحول بعض خصائص حلقات UU و UJ
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