in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras of odd socle degree. In the first open case, namely Hilbert function (1, 3, 6, 6, 3, 1), we give a complete answer in every characteristic by translating the problem to one of...

A certain class of rank two pointed Hopf algebras is considered. The simple modules of their Drinfel’d double is described using Radford’s method [Rad03]. The socle of the tensor product of two such modules is computed and a formula similar to the one in [Che00] is obtained in some conditions. Cases when such a tensor product is completely irreducible are also given in the last section.

Let $$G$$ be a finite group. Its spectrum $$\omega(G)$$ is the set of all element orders . The prime $$\pi(G)$$ divisors order Gruenberg–Kegel graph (or graph) $$\Gamma(G)$$ simple with vertex in which any two vertices $$p$$ and $$q$$ are adjacent if only $$pq\in\omega(G)$$ structural theorem implies that class groups disconnected graphs widely generalizes Frobenius groups, whose role group the...

In this paper we will study artinian quotients A = R/I of the polynomial ring R = k[x1, ..., xr], where k is a field of characteristic zero, the xi’s all have degree 1 and I is a homogeneous ideal of R. These rings are often referred to as standard graded artinian algebras. Before explaining the main results of this work, we establish some of the notation we will use: the h-vector of A is h(A) ...