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1.
Karin Cvetko-Vah 《Semigroup Forum》2004,68(2):268-279
Given a ring $R$, let $S\subseteq R$ be a pure multiplicative band that is
closed under the cubic join operation $x\nabla y = x+y+yx-xyx-yxy.$ We show that
$\left( S,\cdot,\nabla\right) $ forms a pure skew lattice if and only if $S$
satisfies the polynomial identity $\left(xy-yx\right)^{2}z = z\left(xy-yx\right)^{2}$.
We also examine properties of pure skew lattices
in rings. 相似文献
2.
Distributive lattices are well known to be precisely those lattices that possess cancellation: x úy = x úzx \lor y = x \lor z and x ùy = x ùzx \land y = x \land z imply y = z. Cancellation, in turn, occurs whenever a lattice has neither of the five-element lattices M
3 or N
5 as sublattices. In this paper we examine cancellation in skew lattices, where the involved objects are in many ways lattice-like,
but the operations ù\land and ú\lor no longer need be commutative. In particular, we find necessary and sufficient conditions involving the nonoccurrence of potential sub-objects similar to M
3 or N
5 that ensure that a skew lattice is left cancellative (satisfying the above implication) right cancellative (x úz = y úzx \lor z = y \lor z and x ùz = y ùzx \land z = y \land z imply x = y) or just cancellative (satisfying both implications). We also present systems of identities showing that left [right or fully]
cancellative skew lattices form varieties. Finally, we give some positive characterizations of cancellation. 相似文献
3.
Categorical skew lattices are a variety of skew lattices on which the natural partial order is especially well behaved. While most skew lattices of interest are categorical, not all are. They are characterized by a countable family of forbidden subalgebras. We also consider the subclass of strictly categorical skew lattices. 相似文献
4.
A. R. Nasr-Isfahani 《代数通讯》2013,41(3):1337-1349
In this note we study radicals of skew polynomial ring R[x; α] and skew Laurent polynomial ring R[x, x ?1; α], for a skew-Armendariz ring R. In particular, among the other results, we show that for an skew-Armendariz ring R, J(R[x; α]) = N 0(R[x; α]) = Ni?*(R)[x; α] and J(R[x, x ?1; α]) = N 0(R[x, x ?1; α]) = Ni?*(R)[x, x ?1; α]. 相似文献
5.
Karin Cvetko-Vah 《代数通讯》2013,41(1):243-247
In the present note we study internal decompositions of skew lattices. This provides further insight into the structure of skew lattices. Special attention is devoted to skew lattices in rings. 相似文献
6.
For a ring endomorphism α,we introduce α-skew McCoy rings which are generalizations of α-rigid rings and McCoy rings,and investigate their properties.We show that if α t = I R for some positive integer t and R is an α-skew McCoy ring,then the skew polynomial ring R[x;α] is α-skew McCoy.We also prove that if α(1) = 1 and R is α-rigid,then R[x;α]/ x 2 is αˉ-skew McCoy. 相似文献
7.
Wagner Cortes 《代数通讯》2013,41(4):1526-1548
In this article we consider rings R with a partial action α of an infinite cyclic group G on R. We generalize the well-known results about Jacobson rings and strongly Jacobson rings in skew polynomial rings and skew Laurent polynomial rings to partial skew polynomial rings and partial skew Laurent polynomial rings. 相似文献
8.
9.
We prove that if R is a semiprime ring and α is a partial action of an infinite cyclic group on R, then R is right Goldie if and only if R[x; α] is right Goldie if and only if R?x; α? is right Goldie, where R[x; α] (R?x; α?) denotes the partial skew (Laurent) polynomial ring over R. In addition, R?x; α? is semiprime while R[x; α] is not necessarily semiprime. 相似文献
10.
M. Spinks 《Semigroup Forum》2000,61(3):341-345
In [3, Section 2.5] Jonathan Leech asked if the middle distributive identities for skew lattices are independent. This note exhibits a nine element counterexample, found with the model generating program SEM [7]. 相似文献
11.
Cheng-Kai Liu 《Algebras and Representation Theory》2013,16(6):1561-1576
We investigate the commutativity in a (semi-)prime ring R which admits skew derivations δ 1, δ 2 satisfying [δ 1(x), δ 2(y)]?=?[x, y] for all x, y in a nonzero right ideal of R. This result is a natural generalization of Bell and Daif’s theorem on strong commutativity preserving derivations and a recent result by Ali and Huang. 相似文献
12.
13.
Let α be a nonzero endomorphism of a ring R, n be a positive integer and T_n(R, α) be the skew triangular matrix ring. We show that some properties related to nilpotent elements of R are inherited by T_n(R, α). Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring R[x; α]/(x~n), where R[x; α] is the skew polynomial ring. 相似文献
14.
Chen-Lian Chuang 《代数通讯》2013,41(2):527-539
Soient D un corps non nécessairement commutatif et L un sous-corps de D. On établit une condition nécessaire et suffisante pour que le groupe multiplicatif L de L soit d'indice fini dans son normalisateur N dans D. Lorsque la dimension à gauche [D : L]g est un nombre premier, on précise le groupe N/L et la structure de D. 相似文献
15.
本文中对一个斜群环为Dubrovin赋值环给出了一系列等价刻画,并且刻画了一个Dubrovin赋值斜群环的所有素理想. 相似文献
16.
A. R. Nasr-Isfahani 《代数通讯》2013,41(11):4461-4469
For a ring R, endomorphism α of R and positive integer n we define a skew triangular matrix ring T n (R, α). By using an ideal theory of a skew triangular matrix ring T n (R, α) we can determine prime, primitive, maximal ideals and radicals of the ring R[x; α]/ ? x n ?, for each positive integer n, where R[x; α] is the skew polynomial ring, and ? x n ? is the ideal generated by x n . 相似文献
17.
Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given. Among them all the prime
ideals of a Dubrovin valuation skew group ring are characterised.
Received June 8, 1999, Revised June 4, 2001, Accepted July 20, 2001 相似文献
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20.
Let R be a ring.We show in the paper that the subring Un(R) of the upper triangular matrix ring Tn(R) is α-skew Armendariz if and only if R is α-rigid,also it is maximal in some non α-skew Armendariz rings,where α is a ring endomorphism of R with α(1) = 1. 相似文献