Abstract

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 module over C. This chapter focuses on various ways in which the representation theories of finitely generated and large (not finitely generated) modules over an artin algebra are related. While it is still an open question whether the converse is true for arbitrary left artin rings, the converse is settled for artin algebras. Every simple object is finitely presented if A is an artin algebra.

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