# Finitely

### Finitely generated nilpotent groups are finitely presented ...

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 ...

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

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

### When every projective module is a direct sum of finitely ...

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 ...

### 11. Finitely-generated modules

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.

### 10. FINITELY GENERATED ABELIAN GROUPS §10.1. Finitely ...

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

### Free modules, ﬁnitely-generated modules

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

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

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.

### FINITELY-GENERATED ABELIAN GROUPS

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.