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Morphic and principal-ideal group rings [PDF]
Journal of Algebra, 2007 We observe that the class of left and right artinian left and right morphic rings agrees with the class of artinian principal ideal rings. For $R$ an artinian principal ideal ring and $G$ a group, we characterize when $RG$ is a principal ideal ring; for finite groups $G$, this characterizes when $RG$ is a left and right morphic ring.
Thomas J. Dorsey
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On Rings Whose Principal Ideals are Generalized Pure Ideals [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2007 This paper , introduces the notion of a right PIGP-ring (a ring in which every principal ideal of R is a GP-ideal ) with some of their basic properties ; we also give necessary and sufficient conditions for PIGP-rings to be a division ring and a regular ...
Husam Mohammad
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On S-principal right ideal rings
AIMS Mathematics, 2022 Let S be a multiplicative subset of a ring R. A right ideal A of R is referred to as S-principal if there exist an element s∈S and a principal right ideal aR of R such that As⊆aR⊆A.
Jongwook Baeck
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Enveloping algebras that are principal ideal rings [PDF]
Journal of Pure and Applied Algebra, 2017 Let $L$ be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of $L$ is a principal ideal ring if and only if $L$ is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.
SICILIANO, Salvatore, Usefi, Hamid
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On Rings Whose Principal Ideals are Pure [PDF]
AL-Rafidain Journal of Computer Sciences and Mathematics, 2006 In this work, we study rings whose every principal ideal is a right pure. We give some properties of right PIP – rings and the connection between such rings and division rings.
Shaimaa Ahmad
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Principal ideals in matrix rings [PDF]
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences, 1969 Let R be a ring with a unity 1, and let n be a positive integer. It is well-known [3, p. 37]1 that every two-sided ideal of R" (the complete matrix ring of order n over R) is necessarily of the form M", where M is a two-sided ideal of R. Simple examples show that this result no longer holds for one-sided ideals.
Morris Newman, Stephen Pierce
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A class of principal ideal rings arising from the converse of the Chinese remainder theorem [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 Let R be a (nonzero commutative unital) ring. If I and J are ideals of R such that R/I⊕R/J is a cyclic R-module, then I+J=R. The rings R such that R/I⊕R/J is a cyclic R-module for all distinct nonzero proper ideals I and J of R are the following three ...
David E. Dobbs
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Principal Right Ideal Rings [PDF]
Canadian Journal of Mathematics, 1963 This paper is concerned with the recent work of A. W. Goldie (1 ) on principal right ideal rings (p.r.i. rings). We shall prove some of his main structure theorems using the methods of (3) and (4), and in so doing shall weaken some of his hypotheses.
R. E. Johnson
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Insights Into Principal Ideal Rings and Their Hereditary Properties
Journal of MathematicsIn this paper, we investigate principal ideal rings (PIRs). Specifically, we prove that every local PIR is either a 2-strongly Gorenstein semisimple ring or a discrete valuation ring, which leads to the establishment of the Gorenstein hereditary property
Jin Xie +3 more
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Strong Gröbner bases for polynomials over a principal ideal ring [PDF]
, 2001 Gröbner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Gröbner bases, also known as D-bases.
Graham H. Norton, Ana Sălăgean
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