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1.
Let R be a ring and (S, 〈) be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,(R) has a generalized join in S,(R). Several known results follow as consequences of our results. 相似文献
2.
A ring R is called linearly McCoy if whenever linear polynomials f(x), g(x) e R[x]/{0) satisfy f(x)g(x) : O, then there exist nonzero elements r, s ∈ R such that f(x)r : sg(x) =0. For a ring endomorphism α, we introduced the notion of α-skew linearly McCoy rings by considering the polynomials in the skew polynomial ring R[x; α] in place of the ring R[x]. A number of properties of this generalization are established and extension properties of α-skew linearly McCoy rings are given. 相似文献
3.
Let Mbe a monoid. A ring Ris called M-π-Armendariz if whenever α = a1g1+ a2g2+ · · · + angn, β = b1h1+ b2h2+ · · · + bmhm ∈ R[M] satisfy αβ ∈ nil(R[M]), then aibj ∈ nil(R) for all i, j. A ring R is called weakly 2-primal if the set of nilpotent elements in R coincides with its Levitzki radical. In this paper, we consider some extensions of M-π-Armendariz rings and further investigate their properties under the condition that R is weakly 2-primal. We prove that if R is an M-π-Armendariz ring then nil(R[M]) = nil(R)[M]. Moreover, we study the relationship between the weak zip-property (resp., weak APP-property, nilpotent p.p.-property, weak associated prime property) of a ring R and that of the monoid ring R[M] in case R is M-π-Armendariz. 相似文献
4.
In this paper,we study some cases when an amalgamated construction A■~f I of a ring A along an ideal I of a ring B with respect to a ring homomorphism f from A to B,is prime,semiprime,semicommutative,nil-semicommutative and weakly semicommutative. 相似文献
5.
Morita Context环的若干性质 总被引:1,自引:1,他引:0
研究由Morita Contexts所确定的环,讨论它的K-好环性质,弱Semicom-mutative性质,有许多单式正则元性质和广义稳定环性质等. 相似文献
6.
Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG(H)={α ∈ RG|αh = hα for all h ∈ H), which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG(H) is just the central subalgebra Z(RG) of RG. In this note, we show that the set of all H- conjugacy class sums of G forms an R-basis of CRG(H). Furthermore, let N be a normal subgroup of G and γthe natural epimorphism from G to G to G/N. Then γ induces an epimorphism from RG to RG, also denoted by % We also show that if R is a field of characteristic zero, then γ induces an epimorphism from CRG(H) to CRG(H), that is, 7(CRG(H)) = CRG(H). 相似文献
7.
8.
A ring is called clean if every element is a sum of a unit and an idempotent, while a ring is said to be weakly clean if every element is either a sum or a difference of a unit and an idempotent. Commutative weakly clean rings were first discussed by Anderson and Camillo [2] and were extensively investigated by Ahn and Anderson [1], motivated by the work on clean rings. In this paper, weakly clean rings are further discussed with an emphasis on their relations with clean rings. This work shows new interesting connections between weakly clean rings and clean rings. 相似文献
9.
Acta Mathematica Hungarica - The classes of semicommutative, PS I, 2-primal, weakly-2-primal, NI, NR and Dedekind-finite rings form a strictly increasing chain of classes of rings. Examples have... 相似文献
10.
Nielsen [29] proved that all reversible rings are McCoy and gave an example of a semicommutative ring that is not right McCoy. When R is a reversible ring with an (α, δ)-condition, namely (α, δ)-compatibility, we observe that R satisfies a McCoy-type property, in the context of Ore extension R[x; α, δ], and provide rich classes of reversible (semicommutative) (α, δ)-compatible rings. It is also shown that semicommutative α-compatible rings are linearly α-skew McCoy and that linearly α-skew McCoy rings are Dedekind finite. Moreover, several extensions of skew McCoy rings and the zip property of these rings are studied. 相似文献
11.
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. 相似文献
12.
In this work, using an analogue of Sadovskii's fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation F(x) =μx, (μ≥1) for some weakly sequentially continuous, weakly condensing and weakly 1-set weakly contractive operators with different boundary conditions. Correspondingly, we can obtain some applicable fixed point theorems of Leray-Schauder, Altman and Furi-Pera types in the weak topology setting which generalize and improve the corresponding results of [3,15,16]. 相似文献
13.
In this paper, we discuss the concept of fixed point curve for linear interpolations of weakly inward contractions and establish necessary condition for a nonex- pansive mapping to have approximate fixed point property. 相似文献
14.
张春霞 《纯粹数学与应用数学》2008,24(1):121-124
讨论了在约化条件下,比平凡扩张更广泛的一类扩张环的半交换性.通过给出半交换模的定义,得到平凡扩张是半交换环的一个充要条件. 相似文献
15.
称环R为广义2-素环,如果R的幂零元集与上诣零根一致.证明了R上的多项式为单位当且仅当它的常数项是R中的单位而其它系数是幂零的.因此,广义2-素环上的多项式环的稳定度大于一. 相似文献
16.
S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i(A, Ω, p) is equal to nonzero, where i(A, Ω, p) is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe's theorem, Altman's theorem, Petryshyn's theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2]. 相似文献
17.
In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (generalized) bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals. 相似文献
18.
We consider the sufficient and necessary conditions for the formal triangular matrix ring being right minsymmetric,right DS,semicommutative,respectively. 相似文献
19.
As generalization of r-clean rings and weakly clean rings, we define a ring R is weakly r-clean if for any a∈R there exist an idempotent e and a regular element r such that a = r + e or a = r-e. Some properties and examples of weakly r-clean rings are given. Furthermore, we prove the weakly clean rings and weakly r-clean rings are equivalent for abelian rings. 相似文献