On semigroups with maximal conditions

Hotzel, Eckehart

doi:10.1007/bf02195275

Cited by 26 publications

(21 citation statements)

References 6 publications

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“…However, it is unknown whether this holds in general. Some other consequences of this finiteness condition, related to our results, can be found in [64,65,98]. Recall that a ring R (with identity) is said to be a principal right ideal ring if every right ideal Iof R is generated by one element, that is, I = rR for some r ∈ R. Clearly such rings are right Noetherian and this property is inherited by epimorphic images.…”

Section: Comments and Problemsmentioning

confidence: 74%

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Noetherian Semigroup Algebras

Jespers

Okniński

2007

Algebra and Applications

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Algebra and Applications aims to publish well written and carefully refereed monographs with up-to-date information about progress in all fields of algebra, its classical impact on commutative and noncommutative algebraic and differential geometry, K-theory and algebraic topology, as well as applications in related domains, such as number theory, homotopy and (co)homology theory, physics and discrete mathematics. Particular emphasis will be put on state-of-the-art topics such as rings of differential operators, Lie algebras and super-algebras, group rings and algebras, C*algebras, Kac-Moody theory, arithmetic algebraic geometry, Hopf algebras and quantum groups, as well as their applications. In addition, Algebra and Applications will also publish monographs dedicated to computational aspects of these topics as well as algebraic and geometric methods in computer science.

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Section: Comments and Problemsmentioning

confidence: 74%

“…The assertion of the theorem also can be proved if S is a weakly periodic monoid, that is, for every a ∈ S there exists n ≥ 1 such that Sa n S is an idempotent ideal of S, [64] or [119,Theorem 12.6]. In particular, this class includes periodic monoids and regular monoids.…”

Section: General Noetherian Semigroup Algebrasmentioning

confidence: 99%

Noetherian Semigroup Algebras

Jespers

Okniński

2007

Algebra and Applications

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“…But they are needed for the direct limits in question to have the description given. Indeed (Not, as might seem more natural, with the submonoids of M.) (iii) (Open question of Hotzel [89].) If a monoid M has ascending chain condition on left congruences, must M be finitely generated?…”

Section: Definition 918 Ifmentioning

confidence: 99%

An Invitation to General Algebra and Universal Constructions

Bergman

2015

Universitext

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“…Recently, in [5], Dandan, Gould, Quinn-Gregson and Zenab considered the property that the universal right congruence on a semigroup is finitely generated; we refer to such semigroups as finitely connected (see Remark 2.4 for the motivation behind using this term). Semigroups for which every right congruence is finitely generated, called right noetherian semigroups, have received a fair amount of attention (see [10,13,14,18]). Both of these properties have an interesting relationship to finite generation.…”

Section: Introductionmentioning

confidence: 99%