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Odd H-depth and H-separable extensions

Lars Kadison (2012)

Open Mathematics

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

Shriram K. Nimbhorkar, Rupal C. Shroff (2015)

Czechoslovak Mathematical Journal

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

Leonid Vainerman, Jean-Michel Vallin (2012)

Banach Center Publications

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 generalization of Q I -rings

Josef Jirásko (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper rings for which every s -torsion quasi-injective module is weakly s -divisible for a hereditary preradical s 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 T Q I -rings investigated by J. Ahsan and E. Enochs in [1]. Our aim was to generalize some results concerning Q I -rings obtained by J.S. Golan and S.R. L’opez-Permouth in [12]. A characterization of the Q I -property in the...

On a generalization of W*-modules

David P. Blecher, Jon E. Kraus (2010)

Banach Center Publications

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

Mart Abel, Mati Abel (2014)

Topological Algebra and its Applications

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 -radicals

Sodnomkhorloo Tumurbat, Richard Wiegandt (2006)

Mathematica Slovaca

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