Notes on generalized prime and coprime modules. II.
Notes on purities
Notes on radical filters of ideals
Notes on slender prime rings
If is a prime ring such that is not completely reducible and the additive group is not complete, then is slender.
O automorfismech definovaných na okruhu endomorfismů homogenního totálně rozložitelného modulu
Obaly a pokrytí v teorii modulů
Objets Kar-initiaux
Odd H-depth and H-separable extensions
Let C n(A,B) be the relative Hochschild bar resolution groups of a subring B ⊆ A. The subring pair has right depth 2n if C n+1(A,B) is isomorphic to a direct summand of a multiple of C n(A,B) as A-B-bimodules; depth 2n + 1 if the same condition holds only as B-B-bimodules. It is then natural to ask what is defined if this same condition should hold as A-A-bimodules, the so-called H-depth 2n − 1 condition. In particular, the H-depth 1 condition coincides with A being an H-separable extension of B....
Ojective ideals in modular lattices
The concept of an extending ideal in a modular lattice is introduced. A translation of module-theoretical concept of ojectivity (i.e. generalized relative injectivity) in the context of the lattice of ideals of a modular lattice is introduced. In a modular lattice satisfying a certain condition, a characterization is given for direct summands of an extending ideal to be mutually ojective. We define exchangeable decomposition and internal exchange property of an ideal in a modular lattice. It is...
On ℤ/2ℤ-extensions of pointed fusion categories
We give a classification of ℤ/2ℤ-graded fusion categories whose 0-component is a pointed fusion category. A number of concrete examples are considered.
On a certain identitiy satisfied by a derivation and an arbitrary additive mapping. (Summary).
On a certain identity satisfied by a derivation and an arbitrary additive mapping.
On a class of semigroups admitting ring structure.
On a class of strongly quasi injective modules
On a Class with Rings with Inverse Weak Algorithm.
On a Decomposition of Near-rings in a Subdirect sum of Near-fields
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 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 -radicals