On Bernstein Algebras Satisfying Chain Conditions

Our aim in this article is to study Noetherian and Artinian Bernstein algebras. We show that for Bernstein algebras which are either Jordan or nuclear, each of the Noetherian and Artinian conditions implies finite dimensionality. This result fails for general Noetherian or Artinian Bernstein algebras. We also investigate the relationships between the three finiteness conditions: Noetherian, Artinian, and finitely generated. Especially, we prove that Noetherian Bernstein algebras are finitely generated.     

On Galois Algebras Satisfying the Fundamental Theorem

Let B be a Galois algebra over a commutative ring R with Galois group G such that B ^H is a separable subalgebra of B for each subgroup H of G. Then it is shown that B satisfies the fundamental theorem if and only if B is one of the following three types: (1) B is an indecomposable commutative Galois algebra, (2) B = Re ⊕ R(1 ? e) where e and 1 ? e are minimal central idempotents in B, and (3) B is an indecomposable Galois algebra such that for each separable subalgebra A, V _B (A) = ?∑ _g∈G(A) J _g , and the centers of A and B ^G(A) are the same where V _B (A) is the commutator subring of A in B, J _g  = {b ∈ B | bx = g(x)b for each x ∈ B} for a g ∈ G, and G(A) = {g ∈ G | g(a) = a for all a ∈ A}.     

On Homogeneous Weighted Algebras

We extend the concept of the “join” to the case of infinitely many weighted algebras. We study the problem of its uniqueness (up to weighted isomorphism) which gives rise to a natural notion of homogeneous weighted algebras. We show that several classes of weighted algebras coming from genetics are homogeneous and that homogeneity is preserved by duplication. Finally, we examine some well-known weighted algebras satisfying identities, as Bernstein, train, and evolution algebras.     

关于半群环与群环的链条件的等价性

给出了将半群环的链条件转化为群环的链条件的一个定理,并由此将［１］中的结果推广到半群环的情形．     

On Indecomposable Exceptional Modules Over Gentle Algebras

We give a characterization of indecomposable exceptional modules over finite dimensional gentle algebras. As an application, we study gentle algebras arising from an unpunctured surface and show that a class of indecomposable modules related to curves without self-intersections, as exceptional modules, are uniquely determined by their dimension vectors.     

关于标准分层代数的多项式代数的滤链维数

标准分层代数是拟遗传代数的推广,其性质和理论意义受到人们的重视.在本文中,设A是域k上的标准分层代数,我们从特征模的角度,对A的多项式代数A[x]上的滤链维数进行了研究,得到了一些有意义的结果.     

On Serial Noetherian Rings

It is well known that every serial Noetherian ring satisfies the restricted minimum condition. In particular, following Warfield (1975 Warfield , R. B. ( 1975 ). Serial rings and finitely presented modules . J. Algebra 37 : 187 – 222 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]), such a ring is a direct sum of an Artinian ring and hereditary prime rings. The aim of this note is to show that every serial ring having the restricted minimum condition is Noetherian.     

Group Algebras Satisfying a Certain Lie Identity

ABSTRACT

Let K be a field of characteristic p ≠ 2 and let G be any group. A characterization of group algebras KG satisfying the Lie identity [[x,y],[u,v],[z,t]] = 0 for all x,y,u,v,z,t ? KG is obtained.     

Simple Weight Modules of Non-Noetherian Generalized Down-Up Algebras

We classify all simple weight modules of non-Noetherian generalized down-up algebras.     

On the Derived Categories and Quasitilted Algebras

In this paper, we present some results on the bounded derived category of Artin algebras, and in particular on the indecomposable objects in these categories, using homological properties. Given a complex X ^*, we consider the set and we define the application . We give relationships between some homological properties of an algebra and the respective application l. On the other hand, using homological properties again, we determine two subcategories of the bounded derived category of an algebra, which turn out to be the bounded derived categories of quasi-tilted algebras. As a consequence of these results we obtain new characterizations of quasi-tilted and quasi-tilted gentle algebras. Presented by Raymundo Bautista.     

Fixed Ideals of Certain Cartier Algebras Over F-split Toric Algebras

In this article, the ideals of an F-split toric algebra that are fixed by certain Cartier algebra are described, extending the result for normal toric algebras in the author's joint work with K. Schwede and W. Zhang.     

Partition Algebras are Cellular

The partition algebra P(q) is a generalization both of the Brauer algebra and the Temperley–Lieb algebra for q-state n-site Potts models, underpining their transfer matrix formulation on the arbitrary transverse lattices. We prove that for arbitrary field k and any element q k the partition algebra P(q) is always cellular in the sense of Graham and Lehrer. Thus the representation theory of P(q) can be determined by applying the developed general representation theory on cellular algebras and symmetric groups. Our result also provides an explicit structure of P(q) for arbitrary field and implies the well-known fact that the Brauer algebra D(q) and the Temperley–Lieb algebra TL(q) are cellular.     

Level Algebras of Type 2

In this article, we study standard graded Artinian level algebras, in particular those whose socle-vector has type 2. Our main results are: the characterization of the level h-vectors of the form (1, r,…,r, 2) for r ≤ 4; the characterization of the minimal free resolutions associated to each of the h-vectors above when r = 3; a sharp upper-bound (under certain mild hypotheses) for the level h-vectors (1,r,…,a, 2) of arbitrary codimension r and type 2, which depends on the next to last entry a.     

有限复杂度的Koszul代数

首先给出了Koszul代数的张量积的复杂度,然后研究了Koszul遗传代数上的Koszul单列模,并证明了Koszul遗传代数上的Koszul模M的Koszul合成列在同构意义下是唯一的.