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Ext-algebras and derived equivalences

Dag Madsen (2006)

Colloquium Mathematicae

Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.

Extending modules relative to a torsion theory

Semra Doğruöz (2008)

Czechoslovak Mathematical Journal

An R -module M is said to be an extending module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of a type 2 τ -extending module, where τ is a hereditary torsion theory on Mod - R . An R -module M is called type 2 τ -extending if every type 2 τ -closed submodule of M is a direct summand of M . If τ I is the torsion theory on Mod - R corresponding to an idempotent ideal I of R and M is a type 2 τ I -extending R -module, then the question of whether or not M / M I is...

Extensions of G M -rings

Huanyin Chen, Miaosen Chen (2005)

Czechoslovak Mathematical Journal

It is shown that a ring R is a G M -ring if and only if there exists a complete orthogonal set { e 1 , , e n } of idempotents such that all e i R e i are G M -rings. We also investigate G M -rings for Morita contexts, module extensions and power series rings.

Extremal properties for concealed-canonical algebras

Michael Barot, Dirk Kussin, Helmut Lenzing (2013)

Colloquium Mathematicae

Canonical algebras, introduced by C. M. Ringel in 1984, play an important role in the representation theory of finite-dimensional algebras. They also feature in many other mathematical areas like function theory, 3-manifolds, singularity theory, commutative algebra, algebraic geometry and mathematical physics. We show that canonical algebras are characterized by a number of interesting extremal properties (among concealed-canonical algebras, that is, the endomorphism rings of tilting bundles on...

f -derivations on rings and modules

Paul E. Bland (2006)

Commentationes Mathematicae Universitatis Carolinae

If τ is a hereditary torsion theory on 𝐌𝐨𝐝 R and Q τ : 𝐌𝐨𝐝 R 𝐌𝐨𝐝 R is the localization functor, then we show that every f -derivation d : M N has a unique extension to an f τ -derivation d τ : Q τ ( M ) Q τ ( N ) when τ is a differential torsion theory on 𝐌𝐨𝐝 R . Dually, it is shown that if τ is cohereditary and C τ : 𝐌𝐨𝐝 R 𝐌𝐨𝐝 R is the colocalization functor, then every f -derivation d : M N can be lifted uniquely to an f τ -derivation d τ : C τ ( M ) C τ ( N ) .

Currently displaying 921 – 940 of 3959