Lattices over Noetherian algebras

An analog of the reduction theorem for modules over an integrally closed integral domain is proved for torsionfree modules over a semiprimary Noetherian algebra. The result is translated into concrete terms for pseudo-Bass and pseudohereditary algebras, and also used to study the structure of genera.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 604–610, May, 1990.