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$*$ -biregular rings

Christopher J. Duckenfield (1972)

Commentationes Mathematicae Universitatis Carolinae

$(n, d)$ -injective covers, $n$ -coherent rings, and $(n, d)$ -rings

Weiqing Li, Baiyu Ouyang (2014)

Czechoslovak Mathematical Journal

It is known that a ring $R$ is left Noetherian if and only if every left $R$ -module has an injective (pre)cover. We show that $(1)$ if $R$ is a right $n$ -coherent ring, then every right $R$ -module has an $(n, d)$ -injective (pre)cover; $(2)$ if $R$ is a ring such that every $(n, 0)$ -injective right $R$ -module is $n$ -pure extending, and if every right $R$ -module has an $(n, 0)$ -injective cover, then $R$ is right $n$ -coherent. As applications of these results, we give some characterizations of $(n, d)$ -rings, von Neumann regular rings and semisimple rings....

1-amenability of 𝒜(X) for Banach spaces with 1-unconditional bases

A. Blanco (2012)

Studia Mathematica

The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property 𝔸 has in fact the property. Some further ideas on the problem of whether or not amenability (in...

3-dimensional cohomology of the mod p Steenrod algebra.

Tetsuya Aikawa (1980)

Mathematica Scandinavica

(Co)omologia delle Dialgebre

Alessandra Frabetti (1998)

Bollettino dell'Unione Matematica Italiana

(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras

Chao Wang, Xiao Yan Yang (2017)

Czechoslovak Mathematical Journal

Let $Λ = (\begin{matrix} A & M \\ 0 & B \end{matrix})$ be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective $Λ$ -modules under the condition that $M$ is a cocompatible $(A, B)$ -bimodule, we establish a recollement of the stable category $\bar{Ginj (Λ)}$ . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over $Λ$ .