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$n$ -flat and $n$ -FP-injective modules

Xiao Yan Yang, Zhongkui Liu (2011)

Czechoslovak Mathematical Journal

In this paper, we study the existence of the $n$ -flat preenvelope and the $n$ -FP-injective cover. We also characterize $n$ -coherent rings in terms of the $n$ -FP-injective and $n$ -flat modules.

$n$ - $gr$ -coherent rings and Gorenstein graded modules

Mostafa Amini, Driss Bennis, Soumia Mamdouhi (2022)

Czechoslovak Mathematical Journal

Let $R$ be a graded ring and $n \geq 1$ be an integer. We introduce and study the notions of Gorenstein $n$ -FP-gr-injective and Gorenstein $n$ -gr-flat modules by using the notion of special finitely presented graded modules. On $n$ -gr-coherent rings, we investigate the relationships between Gorenstein $n$ -FP-gr-injective and Gorenstein $n$ -gr-flat modules. Among other results, we prove that any graded module in $R$ -gr (or gr- $R$ ) admits a Gorenstein $n$ -FP-gr-injective (or Gorenstein $n$ -gr-flat) cover and preenvelope, respectively....

$N$ -Koszul algebras, a summary.

Green, E.L., Marcos, E.N., Martínez-Villa, R., Zhang, Pu (2003)

AMA. Algebra Montpellier Announcements [electronic only]

$n$ -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

Let $R$ be a graded ring and $n \geq 1$ an integer. We introduce and study $n$ -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that $n$ -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be $m$ -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever $n > m$ . Many properties of the $n$ -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized. Then we investigate...

Natural dualities between abelian categories

Flaviu Pop (2011)

Open Mathematics

In this paper we consider a pair of right adjoint contravariant functors between abelian categories and describe a family of dualities induced by them.

Near-rings in which each prime factor is simple.

Birkenmeier, Gary F., Groenewald, Nico J. (1999)

Mathematica Pannonica

Near-rings with a special condition on idempotents.

Heatherly, H.E., Courville, J.R. (1999)

Mathematica Pannonica

New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.

Carl Faith (1996)

Publicacions Matemàtiques

A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.

Nil-extensions of completely simple semirings

Sunil K. Maity, Rituparna Ghosh (2013)

Discussiones Mathematicae - General Algebra and Applications

A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.

Non-abelian cohomology of associative algebras. The $9$ -term exact sequence

Antonio M. Cegarra, Antonio R. Garzon (1989)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Noncommutative deformations of modules.

Laudal, O.A. (2002)

Homology, Homotopy and Applications

Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers

Robert Lipshitz, David Treumann (2016)

Journal of the European Mathematical Society

Let $A$ be a dg algebra over $𝔽_{2}$ and let $M$ be a dg $A$ -bimodule. We show that under certain technical hypotheses on $A$ , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product $M \otimes_{A}^{L} M$ and converges to the Hochschild homology of $M$ . We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.

Normalizing the cyclic modules of Connes.

W.G. Dwyer, D.M. Kan (1985)

Commentarii mathematici Helvetici

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