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您的检索式：作者名="Zhelin Piao"
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| 1 | A Property Satisfying Reducedness over Centers显示文摘This article concerns a ring property called pseudo-reduced-over-center that is satisfied by free algebras over commutative reduced rings.The properties of radicals of pseudo-reduced-over-center rings are investigated,especially related to polynomial rings.It is proved that for pseudo-reduced-over-center rings of nonzero characteristic,the centers and the pseudo-reduced-over-center property are preserved through factor rings modulo nil ideals.For a locally finite ring R,it is proved that if R is pseudo-reduced-over-center,then R is commutative and R/J(R)is a commutative regular ring with J(R)nil,where J(R)is the Jacobson radical of R. | Hailan Jin Tai Keun Kwak Yang Lee Zhelin Piao | 2021 | Algebra Colloquium2021，28，3： | 0 |
| 2 | Duo Property Applied to Powers and Regular Elements显示文摘The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements.Such rings shall be called right exp-DR.We investigate the structures of group rings,right quotient rings,matrix rings and(skew)polynomial rings,through the study of right exp-DR rings.In addition,we provide a method of constructing finite non-abelian p-groups for any prime p. | TaiKeun Kwak Yang Lee Zhelin Piao Yeonsook Seo | 2023 | Algebra Colloquium2023，30，1： | 0 |
| 3 | Remarks on Centers of Rings显示文摘It is proved that for matrices A,B in the n by n upper triangular matrix ring T_(n)(R)over a domain R,if AB is nonzero and central in T_(n)(R)then AB=BA.The n by n full matrix rings over right Noetherian domains are also shown to have this property.In this article we treat a ring property that is a generalization of this result,and a ring with such a property is said to be weakly reversible-over-center.The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains.The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally.We also consider the connection between the property of being weakly reversible-over-center and the related ring properties. | Juan Huang Hailan Jin Tai Keun Kwak Yang Lee Zhelin Piao | 2021 | Algebra Colloquium2021，28，1： | 0 |
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