Ext-algebras and derived equivalences
Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.
Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.
An -module is said to be an extending module if every closed submodule of is a direct summand. In this paper we introduce and investigate the concept of a type 2 -extending module, where is a hereditary torsion theory on -. An -module is called type 2 -extending if every type 2 -closed submodule of is a direct summand of . If is the torsion theory on - corresponding to an idempotent ideal of and is a type 2 -extending -module, then the question of whether or not is...
It is shown that a ring is a -ring if and only if there exists a complete orthogonal set of idempotents such that all are -rings. We also investigate -rings for Morita contexts, module extensions and power series rings.
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...
We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings.
If is a hereditary torsion theory on and is the localization functor, then we show that every -derivation has a unique extension to an -derivation when is a differential torsion theory on . Dually, it is shown that if is cohereditary and is the colocalization functor, then every -derivation can be lifted uniquely to an -derivation .