共查询到20条相似文献,搜索用时 15 毫秒
1.
We show that π-regular rings and clean rings can be completely characterized by topological properties of their prime spectrums respectively. In addition, we give some applications of those result. Among others, we improve the main result of Samei (2004) and give a new criterion for a clean ring that a commutative ring is clean if and only if idempotents lifts modulo every radical ideal. 相似文献
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N. Yu. Makarenko 《Siberian Mathematical Journal》2005,46(6):1097-1107
We improve the conclusion in Khukhro's theorem stating that a Lie ring (algebra) L admitting an automorphism of prime order p with finitely many m fixed points (with finite-dimensional fixed-point subalgebra of dimension m) has a subring (subalgebra) H of nilpotency class bounded by a function of p such that the index of the additive subgroup |L: H| (the codimension of H) is bounded by a function of m and p. We prove that there exists an ideal, rather than merely a subring (subalgebra), of nilpotency class bounded in terms of p and of index (codimension) bounded in terms of m and p. The proof is based on the method of generalized, or graded, centralizers which was originally suggested in [E. I. Khukhro, Math. USSR Sbornik 71 (1992) 51–63]. An important precursor is a joint theorem of the author and E. I. Khukhro on almost solubility of Lie rings (algebras) with almost regular automorphisms of finite order. 相似文献
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极小条件环中的左理想的因子分解王元金(辽宁师范大学数学系,大连116022)关键词交换环,素理想,左理想.分类号AMS(1991)13A15/CCLO153.3文献[1]讨论了极小条件环中左理想分解为左素理想之交的问题.本文利用文献[1]的一些结果,... 相似文献
5.
研究了循环环R=的理想、素理想和极大理想的个数和结构,得到了如下结论:1)理想:(1)若|R|=∞,则R共有无穷多个理想:;(2)若|R|=n,设n的正因数个数为T(n),则R共有T(n)个理想:.2)素理想:(1)若|R|=∞,设a^2=ka(k≥0),①当k=0时,R的素理想只有R;②当k>0时,R的素理想共有无穷多个,它们是:{0}、R及;(2)若|R|=n>1,设a^2=ka,0≤k.3)极大理想:(1)若|R|=∞,则R有无限多个极大理想,它们是;(2)若|R|=n>1,设n的互不相同的素因数个数为ψ(n),则R共有ψ(n)个极大理想:(pa|p是n的素因数). 相似文献
6.
In this paper we consider serial rings with T-nilpotent prime radical, factor-rings of which by the prime radical are right Noetherian rings. We prove that the prime quiver
of such a ring is a disconnected union of cycles and chains. In the case when the prime quiver of such a serial ring is a
chain the prime radical is nilpotent. For serial rings with nilpotent prime radical we introduce an analogue of Kupisch series.
Presented by Yu. Drozd
Mathematics Subject Classifications (2000) 16P40, 16G10. 相似文献
7.
Xiaofei Qi 《代数通讯》2013,41(10):3824-3835
Let ? be a unital prime ring with characteristic not 2 and containing a nontrivial idempotent P. It is shown that, under some mild conditions, an additive map L on ? satisfies L([A, B]) = [L(A), B] + [A, L(B)] whenever AB = 0 (resp., AB = P) if and only if it has the form L(A) = ?(A) + h(A) for all A ∈ ?, where ? is an additive derivation on ? and h is an additive map into its center. 相似文献
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Given two rings R ? S, S is said to be a minimal ring extension of R, if R is a maximal subring of S. In this article, we study minimal extensions of an arbitrary ring R, with particular focus on those possessing nonzero ideals that intersect R trivially. We will also classify the minimal ring extensions of prime rings, generalizing results of Dobbs, Dobbs &; Shapiro, and Ferrand &; Olivier, on commutative minimal extensions. 相似文献
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I. Alrasasi 《代数通讯》2013,41(4):1385-1400
Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be 𝔹 x (D): = {f ∈ K[X] | ? a ∈ D, f(xX + a) ∈ D[X]}, where x ∈ D. A Bhargava ring over D is a subring of the ring of integer-valued polynomials over D. In this article, we study the prime ideal structure and calculate the Krull and valuative dimension of Bhargava rings over a general domain D. 相似文献
12.
We show that, if a groupoid graded ring has a grading satisfying a certain nondegeneracy property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property. 相似文献
13.
Let T be a complete local (Noetherian) ring with maximal ideal M, P a nonmaximal ideal of T, and C = {Q 1, Q 2,…} a (nonempty) finite or countable set of nonmaximal prime ideals of T. Let {p 1, p 2,…} be a set of nonzero regular elements of T, whose cardinality is the same as that of C. Suppose that p i ∈ Q j if and only if i = j. We give conditions that ensure there is an excellent local unique factorization domain A such that A is a subring of T, the maximal ideal of A is M ∩ A, the (M ∩ A)-adic completion of A is T, and so that the following three conditions hold: (1) p i ∈ A for every i; (2) A ∩ P = (0), and if J is a prime ideal of T with J ∩ A = (0), then J ? P or J ? Q i for some i; (3) for each i, p i A is a prime ideal of A, Q i ∩ A = p i A, and if J is a prime ideal of T with J ? Q i , then J ∩ A ≠ p i A. 相似文献
14.
研究了每一个极大左理想是弱右理想的环的性质.得到了SF-环和强正则环的一些新的刻画,推广了一些已知的结论. 相似文献
15.
Mohammad Ashraf Nadeem-ur-Rehman Shakir Ali 《Southeast Asian Bulletin of Mathematics》2002,25(3):379-382
Let R be a prime ring with characteristic different from two and U be a Lie ideal of R such that u2 U for all u U. In the present paper it is shown that if d is an additive mappings of R into itself satisfying d(u2) = 2ud(u), for all u U, then either U Z(R) or d(U) = (0).1991 Mathematics Subject Classification 16W25 16N60 相似文献
16.
研究了每一个极大左理想是弱右理想的环的性质.得到了左SF-环和强正则环的一些新的刻画,推广了一些已知的结论. 相似文献
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Let 𝒜 be a unital prime ring containing a nontrivial idempotent P. Assume that Φ: 𝒜 → 𝒜 is a nonlinear surjective map. It is shown that Φ preserves strong commutativity if and only if Φ has the form Φ(A) = αA + f(A) for all A ∈ 𝒜, where α ∈ {1, ?1} and f is a map from 𝒜 into 𝒵(𝒜). As an application, a characterization of nonlinear surjective strong commutativity preserving maps on factor von Neumann algebras is obtained. 相似文献
20.
Marcel Erné 《Applied Categorical Structures》2000,8(1-2):115-144
We introduce ideals, radicals and prime ideals in arbitrary algebras with at least one binary operation, and we show that various separation lemmas and prime ideal theorems are special instances of one general theorem which, in turn, is equivalent to the Boolean Prime Ideal Theorem (or Ultrafilter Principle). 相似文献