## Mathematics Subject Classification – MSC2020

History of associative rings and algebras [Consider also classification numbers pertaining to Section 01-XX] 122

Module categories in associative algebras [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 3366

Homological methods in associative algebras {For commutative rings, see 13Dxx; for general categories, see 18Gxx} 10447

Finite rings and finite-dimensional associative algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx} 2839

Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension (associative rings and algebras) 1814

Torsion theories; radicals on module categories (associative algebraic aspects) [See also 13D30, 18E40] {For radicals of rings, see 16Nxx} 1499