Publisher Summary This chapter discusses large modules over artin algebras. An artin ring
Λ is said to be an artin algebra if its center C is an artin ring and Λ is a finitely generated …

INTRODUCTION. An artin algebra is an Artin ring which is a finitely generated module over
its center R, which is also an Artin ring. For an Artin algebra A we denote by mod (A) the …

Let A be an artin algebra over a commutative artin ring R and mod A be the category of
finitely generated right A-modules. A cycle in mod A is a sequence of non-zero non …

Throughout this paper A denotes an artin algebra over a commutative artin ring R; ie, A is an
R-algebra which is finitely generated as an R-module. All A-modules are assumed to …

Throughout this note, all rings will be self-basic connected artin algebras over a fixed
commutative local artin ring k and all modules will be finitely generated. Homomorphisms …

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms,
indecomposable finitely generated Gorenstein-projective A-modules. We prove that for a …

Let A be an artin algebra over a commutative artin ring R, mod A be the category of finitely
generated right A-modules, and rad∞(modA) be the infinite power of the Jacobson radical …

Let C be a skeletally small abelian category with only a finite number of non-isoaorphic
simple objects and such that each object in C has finite length. Then C has a finite number of …

Having initiated the study of graded Artin algebras A in [91, here we initiate the study of their
representation theory. Our point of view is to study graded/i-modules, which we believe to be …

Generic modules were introduced by Crawley-Boevey in order to provide a better
understanding of finite-dimensional algebras of tame representation type. In fact he has …