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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....

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 -Kasch spaces

Ali Akbar Estaji, Melvin Henriksen (2010)

Archivum Mathematicum

If X is a Tychonoff space, C ( X ) its ring of real-valued continuous functions. In this paper, we study non-essential ideals in C ( X ) . Let a be a infinite cardinal, then X is called a -Kasch (resp. a ¯ -Kasch) space if given any ideal (resp. z -ideal) I with gen ( I ) < a then I is a non-essential ideal. We show that X is an 0 -Kasch space if and only if X is an almost P -space and X is an 1 -Kasch space if and only if X is a pseudocompact and almost P -space. Let C F ( X ) denote the socle of C ( X ) . For a topological space X with only...

On a theorem of McCoy

Rajendra K. Sharma, Amit B. Singh (2024)

Mathematica Bohemica

We study McCoy’s theorem to the skew Hurwitz series ring ( HR , ω ) for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring R satisfies McCoy’s theorem of skew Hurwitz series.

On algebras of generalized Latin squares

František Katrnoška (2011)

Mathematica Bohemica

The main result of this paper is the introduction of a notion of a generalized R -Latin square, which includes as a special case the standard Latin square, as well as the magic square, and also the double stochastic matrix. Further, the algebra of all generalized Latin squares over a commutative ring with identity is investigated. Moreover, some remarkable examples are added.

On category 𝒪 for cyclotomic rational Cherednik algebras

Iain G. Gordon, Ivan Losev (2014)

Journal of the European Mathematical Society

We study equivalences for category 𝒪 p of the rational Cherednik algebras 𝐇 p of type G ( n ) = ( μ ) n 𝔖 n : a highest weight equivalence between 𝒪 p and 𝒪 σ ( p ) for σ 𝔖 and an action of 𝔖 on an explicit non-empty Zariski open set of parameters p ; a derived equivalence between 𝒪 p and 𝒪 p ' whenever p and p ' have integral difference; a highest weight equivalence between 𝒪 p and a parabolic category 𝒪 for the general linear group, under a non-rationality assumption on the parameter p . As a consequence, we confirm special cases of conjectures...

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