# Ascending chain conditions on right ideals of semigroups

@inproceedings{Miller2022AscendingCC, title={Ascending chain conditions on right ideals of semigroups}, author={Craig Miller}, year={2022} }

. We call a semigroup S right noetherian if it satisﬁes the ascending chain condition on right ideals, and we say that S satisﬁes ACCPR if it satisﬁes the ascending chain condition on principal right ideals. We investigate the behavior of these two conditions with respect to ideals and ideal extensions, with a particular focus on minimal and 0-minimal one-sided ideals. In particular, we show that the property of satisfying ACCPR is inherited by right and left ideals. On the other hand, we…

## References

SHOWING 1-10 OF 29 REFERENCES

### Ascending chain conditions on principal left and right ideals for semidirect products of semigroups

- Mathematics
- 2012

In this paper we investigate the ascending chain conditions on principal left and right ideals for semidirect products of semigroups and show how this is connected to the corresponding problem for…

### Semigroups whose right ideals are finitely generated

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2021

Abstract We call a semigroup $S$ weakly right noetherian if every right ideal of $S$ is finitely generated; equivalently, $S$ satisfies the ascending chain condition on right ideals. We provide an…

### Right noetherian semigroups

- MathematicsInt. J. Algebra Comput.
- 2020

This paper discusses how semigroups relate to their substructures with regard to the property of being right noetherian, and investigates whether this property is preserved under various semigroup constructions.

### The Ascending Chain Condition for Principal Ideals of Rings of Generalized Power Series

- Mathematics
- 2004

Abstract Let (S, ≤) be a strictly totally ordered monoid and R a domain. It is shown in this paper that [[R S,≤]], the ring of generalized power series with coefficients in R and exponents in S,…

### Chain conditions on commutative monoids

- MathematicsSemigroup Forum
- 2019

We consider commutative monoids with some kinds of isomorphism condition on their ideals. We say that a monoid S has isomorphism condition on its ascending chains of ideals, if for every ascending…

### The ascending chain condition for principal left or right ideals of skew generalized power series rings

- Mathematics
- 2016

Let $R$ be a ring, $(S,\leq)$ a strictly ordered monoid and $\omega: S\rightarrow End(R)$ a monoid homomorphism. In this paper we study the ascending chain conditions on principal left (resp. right)…

### Fundamentals of semigroup theory

- Mathematics
- 1995

1. Introductory ideas 2. Green's equivalences regular semigroups 3. 0-simple semigroups 4. Completely regular semigroups 5. Inverse semigroups 6. Other classes of regular semigroups 7. Free…

### String-Rewriting Systems

- Computer ScienceText and Monographs in Computer Science
- 1993

This chapter provides formal definitions of string-rewriting systems and their induced reduction relations and Thue congruences and relies on Section 1.4 for basic definitions and notation for strings.