共查询到20条相似文献,搜索用时 78 毫秒
1.
Let R be a reduced commutative ring with 1 ≠ 0. Let R E be the set of equivalence classes for the equivalence relation on R given by x ~ y if and only if ann R (x) = ann R (y). Then R E is a (meet) semilattice with respect to the order [x] ≤ [y] if and only if ann R (y) ? ann R (x). In this paper, we investigate when R E is a lattice and relate this to when R is weakly complemented or satisfies the annihilator condition. We also consider when R is a (meet) semilattice with respect to the Abian order defined by x ≤ y if and only if xy = x 2. 相似文献
2.
In this article, we define a new associative dialgebra over a polynomial algebra F[x, y] with two indeterminates x and y. Left derivations, right derivations, derivations, and automorphisms of F[x, y] as associative dialgebra are determined. Meanwhile, we also determine all homogeneous derivations of F[x, y] as ?-graded Leibniz algebra, and automorphisms of Leibniz algebra F[x, y] preserving the standard filtration. 相似文献
3.
We construct the endofunctor 𝔲𝔠𝔢 between the category of Leibniz algebras which assigns to a perfect Leibniz algebra its universal central extension, and we obtain the isomorphism 𝔲𝔠𝔢Lie(𝔮Lie) ? (𝔲𝔠𝔢Leib(𝔮))Lie, where 𝔮 is a perfect Leibniz algebra satisfying the condition [x, [x, y]] + [[x, y], x] = 0, for all x, y ∈ 𝔮. Moreover, we obtain several results concerning the lifting of automorphisms and derivations in a covering. We also study the relationship between the universal central extension of a semidirect product of perfect Leibniz algebras and the semidirect product of the universal central extension of both of them. 相似文献
4.
《代数通讯》2013,41(5):2053-2065
Abstract We consider the group G of C-automorphisms of C(x, y) (resp. C[x, y]) generated by s, t such that t(x) = y, t(y) = x and s(x) = x, s(y) = ? y + u(x) where u ∈ C[x] is of degree k ≥ 2. Using Galois's theory, we show that the invariant field and the invariant algebra of G are equal to C. 相似文献
5.
Mitsuhiro Miyazaki 《代数通讯》2013,41(9):2894-2900
Let K be a field, D a finite distributive lattice and P the set of all join-irreducible elements of D. We show that if {y ∈ P | y ≥ x} is pure for any x ∈ P, then the Hibi ring ? K (D) is level. Using this result and the argument of sagbi basis theory, we show that the homogeneous coordinate rings of Schubert subvarieties of Grassmannians are level. 相似文献
6.
Surjeet Kour 《代数通讯》2013,41(9):4066-4083
If k is a field of characteristic zero, c ∈ k?{0}, s, t ≥ 1, and r ≥ 0 are integers, then it is shown that the k-derivation y r ? x + (y s x t + c)? y of the polynomial algebra k[x, y] is simple. 相似文献
7.
Dominik Benkovič 《代数通讯》2018,46(5):1859-1867
For a triangular algebra 𝒜 and an automorphism σ of 𝒜, we describe linear maps F,G:𝒜→𝒜 satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈𝒜 are such that xy = 0. In particular, when 𝒜 is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈𝒜, where D:𝒜→𝒜 is a skew derivation. When 𝒜 is not zero product determined, we show that there are also nonstandard solutions for maps F and G. 相似文献
8.
9.
Ilinka Dimitrova 《代数通讯》2013,41(5):1821-1826
A partial transformation α on an n-element chain X n is called order-preserving if x ≤ y implies xα ≤yα for all x, y in the domain of α and it is called extensive if x ≤ xα for all x in the domain of α. The set of all partial order-preserving extensive transformations on X n forms a semiband POE n . We determine the maximal subsemigroups as well as the maximal subsemibands of POE n . 相似文献
10.
Mateja Grašič 《Linear and Multilinear Algebra》2013,61(8):1007-1022
We show that the Lie algebra ? of skew-symmetric matrices with respect to either transpose or symplectic involution is zero product determined. This means that every bilinear map {·,·} from ? × ? into a vector space X is of the form {x, y} = T ([x, y]) for some linear map T provided that the following condition is fulfilled: [x, y] = 0 implies {x, y} = 0. 相似文献
11.
Jose Brox Esther García Miguel Gómez Lozano 《Mediterranean Journal of Mathematics》2014,11(4):1061-1067
In this paper, we prove that the ideals generated by two elements x, y in a nondegenerate Lie algebra L over a ring of scalars Φ with \({\frac 1 2, \frac 1 3}\) are orthogonal if and only if [x, [y, L]] = 0. 相似文献
12.
13.
Ari Vesanen 《代数通讯》2013,41(4):1177-1195
ABSTRACT We introduce the notion of weak transitivity for torsion-free abelian groups. A torsion-free abelian group G is called weakly transitive if for any pair of elements x, y ∈ G and endomorphisms ?, ψ ∈ End(G) such that x? = y, yψ = x, there exists an automorphism of G mapping x onto y. It is shown that every suitable ring can be realized as the endomorphism ring of a weakly transitive torsion-free abelian group, and we characterize up to a number-theoretical property the separable weakly transitive torsion-free abelian groups. 相似文献
14.
The nilpotent graph of a group G is a simple graph whose vertex set is G?nil(G), where nil(G) = {y ∈ G | ? x, y ? is nilpotent ? x ∈ G}, and two distinct vertices x and y are adjacent if ? x, y ? is nilpotent. In this article, we show that the collection of finite non-nilpotent groups whose nilpotent graphs have the same genus is finite, derive explicit formulas for the genus of the nilpotent graphs of some well-known classes of finite non-nilpotent groups, and determine all finite non-nilpotent groups whose nilpotent graphs are planar or toroidal. 相似文献
15.
A. Joseph Kennedy 《代数通讯》2013,41(1):145-170
In this article, we study an important subalgebra of the tensor product partition algebra P k (x)? P k (y), denoted by P k (x, y) and called “Class Partition Algebra.” We show that the algebra P k (n, m) is the centralizer algebra of the wreath product S m ? S n . Furthermore, the algebra P k (x, y) and the tensor product partition algebra P k (x)? P k (y) are subalgebras of the G-colored partition algebra P k (x;G) and G-vertex colored partition algebra P k (x, G) respectively, for every group G with |G|=y ≥ 2k. 相似文献
16.
Petter Andreas Bergh 《代数通讯》2013,41(11):3440-3450
We compute the Hochschild cohomology and homology of the algebra Λ = k 〈x, y〉/(x 2, xy + qyx, y 2) with coefficients in 1 Λψ for every degree preserving k-algebra automorphism ψ : Λ → Λ. As a result we obtain several interesting examples of the homological behavior of Λ as a bimodule. 相似文献
17.
18.
We associate a graph 𝒩 G with a group G (called the non-nilpotent graph of G) as follows: take G as the vertex set and two vertices are adjacent if they generate a non-nilpotent subgroup. In this article, we study the graph theoretical properties of 𝒩 G and its induced subgraph on G \ nil(G), where nil(G) = {x ∈ G | ? x, y ? is nilpotent for all y ∈ G}. For any finite group G, we prove that 𝒩 G has either |Z*(G)| or |Z*(G)| +1 connected components, where Z*(G) is the hypercenter of G. We give a new characterization for finite nilpotent groups in terms of the non-nilpotent graph. In fact, we prove that a finite group G is nilpotent if and only if the set of vertex degrees of 𝒩 G has at most two elements. 相似文献
19.
20.
Jie Meng 《Semigroup Forum》1995,50(1):89-96
Chan and Shum [2] introduced the notion of implicative semigroups and obtained some of its important properties. BCK algebras
with condition (S) were introduced by Iséki [4] and extensively investigated by several authors. In this note, we prove that
implicative commutative semigroups are equivalent to BCK algebras with condition (S), that is, given an algebra <S;≤,·,*,1> of type (2,2,0), define ⊗ by stipulatingx⊗y=y*x and ≺ by puttingx≺y if and only ify≤x, then <S≤,·,*,1> is an implicative commutative semigroup if and only if <S;≺,·,⊗, 1> is a BCK algebra with condition (S); a nonempty subsetF ofS is an ordered filter of <S;≤,·,*, 1> if and only ifF is an ideal of <S;≺,·, ⊗, 1>.
The author would like to thank the referee for his valuable comments which helped in the modification of this paper. 相似文献