Regular sequences and lifting property

Manfred Herrmann and Rolf Schmidt

Vol. 75 (1978), No. 2, 449–453

DOI: 10.2140/pjm.1978.75.449

Abstract

Let A be a commutative noetherian ring, E a finite A-module and let M be an arbitrary A-module. Let φ : E → M be a homomorphisn of A-modules.

In this note we prove in an elementary way that an M-sequence x = (x₁,⋯,x_n) being taken to lie in the (Jacobson-) radical rad (A) of A, is also an E-sequence if xE is the contraction φ⁻¹(xM) of xM in E.

Mathematical Subject Classification 2000

Primary: 13C99

Milestones

Received: 20 April 1977

Published: 1 April 1978