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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.

New evidence for Green's conjecture on syzygies of canonical curves

A. Hirschowitz, S. Ramanan (1998)

Annales scientifiques de l'École Normale Supérieure

Noether-Lefschetz, space curves and mathematical instantons.

Angelo Felice Lopez (1994)

Mathematische Annalen

Nonflat deformations of modules and isolated singularities.

Hartwig von Essen (1990)

Mathematische Annalen

Notes on generalizations of Bézout rings

Haitham El Alaoui, Hakima Mouanis (2021)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we give new characterizations of the $P$ - $2$ -Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non- $2$ -Bézout $P$ - $2$ -Bézout rings and examples of non- $P$ -Bézout $P$ - $2$ -Bézout rings.

Notes on the multiplicity conjecture.

Jürgen Herzog, Xinxian Zheng (2006)

Collectanea Mathematica

New cases of the multiplicity conjecture are considered.

Numerical characters of graded algebras

Giuseppe Valla (2004)

Bollettino dell'Unione Matematica Italiana

This is the summary of the plenary talk I gave in Milan at the XVII Meeting of the Unione Matematica Italiana. We focus on some relevant numerical characters of the standard graded algebras and, in some case, we explain their geometric meaning.