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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 class of free Galois extensions.

Deng, X.D., Szeto, G. (1994)

Portugaliae Mathematica

On a Class with Rings with Inverse Weak Algorithm.

Paul M. Cohn (1970)

Mathematische Zeitschrift

On a Conjecture of Zassenhaus on Torsion Units in Integral Group Rings.

Jürgen Ritter, Sudarshan K. Sehgal (1983)

Mathematische Annalen

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. $\bar{a}$ -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 $ℵ_{0}$ -Kasch space if and only if $X$ is an almost $P$ -space and $X$ is an $ℵ_{1}$ -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 a variant of quasi-injectivity via kernel functors

Paramhans, S.A. (1988)

Portugaliae mathematica

On abelian separable extensions and Galois sets of rings

G. Szeto, Linjun Ma (1989)

Matematički Vesnik

On algebraically compact semigroup rings.

I.B. Kozhukhov, A.V. Klyushin (1989)

Semigroup forum

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 automorphism group of free quadratic extensions over a ring.

Szeto, George (1984)

International Journal of Mathematics and Mathematical Sciences

On Azumaya Galois extensions and skew group rings.

Szeto, George (1999)

International Journal of Mathematics and Mathematical Sciences

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 $G_{ℓ} (n) = {(μ_{ℓ})}^{n} ⋊ 𝔖_{n}$ : a highest weight equivalence between $𝒪_{p}$ and $𝒪_{σ (p)}$ for $σ \in 𝔖_{ℓ}$ and an action of $𝔖_{ℓ}$ 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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