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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....

$N$ -groups with acc on annihilators and some topological properties.

Chowdhury, K.C., Das, G.C. (2004)

Mathematica Pannonica

$N$ -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.

Natural endomorphisms of quasi-shuffle Hopf algebras

Jean-Christophe Novelli, Frédéric Patras, Jean-Yves Thibon (2013)

Bulletin de la Société Mathématique de France

The Hopf algebra of word-quasi-symmetric functions ( $𝐖𝐐𝐒𝐲𝐦$ ), a noncommutative generalization of the Hopf algebra of quasi-symmetric functions, can be endowed with an internal product that has several compatibility properties with the other operations on $𝐖𝐐𝐒𝐲𝐦$ . This extends constructions familiar and central in the theory of free Lie algebras, noncommutative symmetric functions and their various applications fields, and allows to interpret $𝐖𝐐𝐒𝐲𝐦$ as a convolution algebra of linear endomorphisms of quasi-shuffle...