Gary Brookfield

CANCELLATION IN PRIMELY GENERATED REFINEMENT MONOIDS

Abstract. We prove that any primely generated refinement monoid M has separative cancellation, and even strong separative cancellation provided M has no nonzero idempotents. A form of multiplicative cancellation also holds:

THE LENGTH OF NOETHERIAN MODULES

na\leq nb

Noetherian Generalized Power Series Rings

implies

Yet Another Elementary Solution of the Brachistochrone Problem

a\leq b

The Length of Noetherian Polynomial Rings

for

The Coefficients of Cyclotomic Polynomials

a,b \in M

Convex Polytopes and Factorization Properties in Generalized Power Series Domains

and

The Extensional Structure of Commutative Noetherian Rings

n \in \{1,2,3,\ldots\}

Direct Sum Cancellation of Noetherian Modules

. In addition, M is a semilattice in the sense that, given

Factoring Quartic Polynomials: A Lost Art

c_1,c_2 \in M