Let D be an integral domain, ψ（D） （resp., t-ψ（D）） be the set of all valuation （resp., t-valuation） ideals of D, and w-P（D） be the set of primary w-ideals of D. Let D[X] be the polynomial ring over 19, c（f...Let D be an integral domain, ψ（D） （resp., t-ψ（D）） be the set of all valuation （resp., t-valuation） ideals of D, and w-P（D） be the set of primary w-ideals of D. Let D[X] be the polynomial ring over 19, c（f） be the ideal of D generated by the coefficients of f ∈ D[X], and Nv = {f∈ D[X] ｜ c（f）v = D}. In this paper, we study integral domains D in which w-P（D） t-ψ（D）, t-ψ（D） w-P（D）, or t-ψ（D） = w-P（D）. We also study the relationship between t-ψ（D） and ψ（D[X]Nv）, and characterize when t-ψ（A ＋ XB[X]） w-P（A ＋ XB[X]） holds for a proper extension A c B of integral domains.展开更多
Let R be a domain and let Rwg be the w-global transform of R. In this note it is shown that if R is a Mori domain, then the t-dimension formula t-dim（Rwg） = t-dim（R） - 1 holds.
For an ordered field (K,T) and an idealI of the polynomial ring $K\left[ {x_1 , \cdots ,x_n } \right]$ , the construction of the generalized real radical $^{\left( {T,U,W} \right)} \sqrt I $ ofI is investigated. When ...For an ordered field (K,T) and an idealI of the polynomial ring $K\left[ {x_1 , \cdots ,x_n } \right]$ , the construction of the generalized real radical $^{\left( {T,U,W} \right)} \sqrt I $ ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing $^{\left( {T,U,W} \right)} \sqrt I $ is presented.展开更多
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
文摘Let D be an integral domain, ψ（D） （resp., t-ψ（D）） be the set of all valuation （resp., t-valuation） ideals of D, and w-P（D） be the set of primary w-ideals of D. Let D[X] be the polynomial ring over 19, c（f） be the ideal of D generated by the coefficients of f ∈ D[X], and Nv = {f∈ D[X] ｜ c（f）v = D}. In this paper, we study integral domains D in which w-P（D） t-ψ（D）, t-ψ（D） w-P（D）, or t-ψ（D） = w-P（D）. We also study the relationship between t-ψ（D） and ψ（D[X]Nv）, and characterize when t-ψ（A ＋ XB[X]） w-P（A ＋ XB[X]） holds for a proper extension A c B of integral domains.
基金Supported by the National Natural Science Foundation of China (Grant No. 10671137)the Research Foun-dation for Doctor Programme (Grant No. 20060636001)
文摘Let R be a domain and let Rwg be the w-global transform of R. In this note it is shown that if R is a Mori domain, then the t-dimension formula t-dim（Rwg） = t-dim（R） - 1 holds.
基金Supported by the National Natural Science Foundation of China（11161006, 11171142） Supported by the Natural Science Foundation of Guangxi Province（2011GXNSFA018144, 018139, 2010GXNSFB 013048, 0991102）+2 种基金 Supported by the Guangxi New Century 1000 Talents Project Supported by the Guangxi Graduate Student Education Innovation Project（2011106030701M06） Supported by the SRF of Guangxi Education Committee
文摘In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19661002)the Climbing Project
文摘For an ordered field (K,T) and an idealI of the polynomial ring $K\left[ {x_1 , \cdots ,x_n } \right]$ , the construction of the generalized real radical $^{\left( {T,U,W} \right)} \sqrt I $ ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing $^{\left( {T,U,W} \right)} \sqrt I $ is presented.
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.
