• Corpus ID: 252568251

Arithmetic of additively reduced monoid semidomains

@inproceedings{Chapman2022ArithmeticOA,
  title={Arithmetic of additively reduced monoid semidomains},
  author={Scott T. Chapman and Harold Polo},
  year={2022}
}
. A subset S of an integral domain R is called a semidomain if the pairs ( S, +) and ( S, · ) are semigroups with identities; additionally, we say that S is additively reduced provided that S contains no additive inverses. Given an additively reduced semidomain S and a torsion-free monoid M , we denote by S [ M ] the semidomain consisting of polynomial expressions with coefficients in S and exponents in M ; we refer to these objects as additively reduced monoid semidomains. We study the… 

References

SHOWING 1-10 OF 31 REFERENCES

Bi-atomic classes of positive semirings

A subsemiring S of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}

Length-factoriality in commutative monoids and integral domains

When Is a Puiseux Monoid Atomic?

This work surveys some of the most relevant aspects related to the atomicity of Puiseux monoids and provides characterizations of when M is finitely generated, factorial, half-factorial, other-half- Factorial, Prüfer, seminormal, root-closed, and completely integrally closed.

Factorizations in upper triangular matrices over information semialgebras

On the atomicity of monoid algebras

Half-factorial-domains

LetR be a commutative domain with 1. We termR an HFD (Half-Factorial-Domain) provided the equality Πi=1nχi=Π{f=1/m}yf impliesm=n, whenever thex’s and they’s are non-zero, non-unit and irreducible

Polynomial extensions of atomic domains

Finiteness theorems for factorizations