**Finitely** generated nilpotent groups are **finitely** presented and residually finite StephenG. Simpson First draft: March 18,2005 This draft: April 8,2005 Definition1.

bulletin of the american mathematical society volume 81, number 4, july 1975 **finitely** embedded modules over noetherian rings by s. m. ginn and p. b. moss

**FINITELY** ADDITIVE MEASURES BY KÔSAKU YOSIDA AND EDWIN HEWITT 0. Introduction. The present paper is concerned with real-valued meas-ures which enjoy the property of finite additivity but not necessarily the

Journal of Algebra 315 (2007) 454-481 www.elsevier.com/locate/jalgebra When every projective module is a direct sum of **finitely** generated module s Warren Wm. McGovern a, Gena Puninski b, Philipp Rothmaler c , ∗ a Department of Mathematics and Statistics, Bowling Green State University ...

174 **Finitely**-generated modules [3.0.1]Theorem: A principal ideal domain is a unique factorization domain. Before proving this, there are relatively elementary remarks that are of independent interest, and useful in the proof.

171 10. **FINITELY** GENERATED ABELIAN GROUPS §10.1. **Finitely** Presented Abelian Groups The group A, B, C | A 4 = B 2 = 1, AB = BA, AC = CA, BC = CB is an example of a

**Finitely**-generated modules over a domain In the sequel, the results will mostly require that R be a domain, or, more stringently, a principal ideal

COMMUTATIVENOETHERIAN SEMIGROUPS ARE **FINITELY** GENERATED GARYBROOKFIELD Abstract. We provide a short proof that a commutative semigroup is **finitely** generated if its lattice of congruences is Noetherian.

THE FUNDAMENTAL THEOREM OF **FINITELY** GENERATED ABELIAN GROUPS 3 We have shown that if we begin withamapf: Z n! Ggivenbythe matrix M, then we can perform any combination of row and column operations on Mwithout changing the cokernel.

2 **FINITELY**-GENERATED ABELIAN GROUPS Relation transposition. Exchange the i thandthejth relations. Here again i;j 2f1; ;rgwithj 6=i. In symbols, r i $r j.