On a characterization of Azumaya algebras.
A direct proof of Braun's characterization of Azumaya algebras is given.
On a class of free Galois extensions.
On a class of near-rings sum of near-fields
On a class of semigroups admitting ring structure.
On a class of strongly quasi injective modules
On a class of tame symmetric algebras having only periodic modules
On a Class with Rings with Inverse Weak Algorithm.
On a conjecture of Vukman.
On a Conjecture of Zassenhaus on Torsion Units in Integral Group Rings.
On a cubic Hecke algebra associated with the quantum group
We define an operator α on ℂ³ ⊗ ℂ³ associated with the quantum group , which satisfies the Yang-Baxter equation and a cubic equation (α² - 1)(α + q²) = 0. This operator can be extended to a family of operators on with 0 ≤ j ≤ n - 2. These operators generate the cubic Hecke algebra associated with the quantum group . The purpose of this note is to present the construction.
On a Decomposition of Near-rings in a Subdirect sum of Near-fields
On a family of vector space categories
In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers....
On a generalization of -rings
In this paper rings for which every -torsion quasi-injective module is weakly -divisible for a hereditary preradical are characterized in terms of the properties of the corresponding lattice of the (hereditary) preradicals. In case of a stable torsion theory these rings coincide with -rings investigated by J. Ahsan and E. Enochs in [1]. Our aim was to generalize some results concerning -rings obtained by J.S. Golan and S.R. L’opez-Permouth in [12]. A characterization of the -property in the...
On a generalization of W*-modules
a recent paper of the first author and Kashyap, a new class of Banach modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize Hilbert spaces. In the present paper, we describe these modules, giving some motivation, and we prove several new results about them.
On -Kasch spaces
If is a Tychonoff space, its ring of real-valued continuous functions. In this paper, we study non-essential ideals in . Let be a infinite cardinal, then is called -Kasch (resp. -Kasch) space if given any ideal (resp. -ideal) with then is a non-essential ideal. We show that is an -Kasch space if and only if is an almost -space and is an -Kasch space if and only if is a pseudocompact and almost -space. Let denote the socle of . For a topological space with only...
On a problem of Bertram Yood
In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.
On a problem of commutativity of automorphisms.
On -radicals
On a refinement in the classification of the nil rings
On a separation of orbits in the module variety for domestic canonical algebras
Given a pair M,M' of finite-dimensional modules over a domestic canonical algebra Λ, we give a fully verifiable criterion, in terms of a finite set of simple linear algebra invariants, deciding if M and M' lie in the same orbit in the module variety, or equivalently, if M and M' are isomorphic.