In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, th...In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.展开更多
A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to...A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H（R） andT（R,a）. The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent： that is R is pseudo weakly clean; there is an integer n such thatR[x]/（x^n） is pseudo weakly clean; there is an integer n such that R[[x]]/（x^n） is pseudo weakly clean.展开更多
The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algeb...The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed.Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.展开更多
The concept of reflexive property is introduced by Mason. This note concerns a ring-theoretic property of matrix rings over reflexive rings. We introduce the concept of weakly reflexive rings as a generalization of re...The concept of reflexive property is introduced by Mason. This note concerns a ring-theoretic property of matrix rings over reflexive rings. We introduce the concept of weakly reflexive rings as a generalization of reflexive rings. From any ring, we can construct weakly reflexive rings but not reflexive, using its lower nilradical. We study various useful properties of such rings in relation with ideals in matrix rings, showing that this new property is Morita invariant. We also investigate the weakly reflexive property of several sorts of ring extensions which have roles in ring theory.展开更多
Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module...Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.展开更多
基金Foundationitem:The NNSP(19971073) of China and the NSF of Yangzhou University
文摘In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.
文摘A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H（R） andT（R,a）. The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent： that is R is pseudo weakly clean; there is an integer n such thatR[x]/（x^n） is pseudo weakly clean; there is an integer n such that R[[x]]/（x^n） is pseudo weakly clean.
基金supported by a grant from the National Science Foundation.
文摘The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed.Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.
文摘The concept of reflexive property is introduced by Mason. This note concerns a ring-theoretic property of matrix rings over reflexive rings. We introduce the concept of weakly reflexive rings as a generalization of reflexive rings. From any ring, we can construct weakly reflexive rings but not reflexive, using its lower nilradical. We study various useful properties of such rings in relation with ideals in matrix rings, showing that this new property is Morita invariant. We also investigate the weakly reflexive property of several sorts of ring extensions which have roles in ring theory.
基金This research is in part supported by a grant from IPM.
文摘Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.
