Matches in SemOpenAlex for { <https://semopenalex.org/work/W4221156912> ?p ?o ?g. }
Showing items 1 to 43 of
43
with 100 items per page.
- W4221156912 abstract "A semigroup $langle Crangle$ in $mathbb{N}^n$ is a gluing of $langle Arangle$ and $langle Brangle$ if its finite set of generators $C$ splits into two parts, $C=k_1Asqcup k_2B$ with $k_1,k_2geq 1$, and the defining ideals of the corresponding semigroup rings satisfy that $I_C$ is generated by $I_A+I_B$ and one extra element. Two semigroups $langle Arangle$ and $langle Brangle$ can be glued if there exist positive integers $k_1,k_2$ such that, for $C=k_1Asqcup k_2B$, $langle Crangle$ is a gluing of $langle Arangle$ and $langle Brangle$. Although any two numerical semigroups, namely semigroups in dimension $n=1$, can always be glued, it is no longer the case in higher dimensions. In this paper, we give necessary and sufficient conditions on $A$ and $B$ for the existence of a gluing of $langle Arangle$ and $langle Brangle$, and give examples to illustrate why they are necessary. These generalize and explain the previous known results on existence of gluing. We also prove that the glued semigroup $langle Crangle$ inherits the properties like Gorenstein or Cohen-Macaulay from the two parts $langle Arangle$ and $langle Brangle$." @default.
- W4221156912 created "2022-04-03" @default.
- W4221156912 creator A5008189220 @default.
- W4221156912 creator A5072916907 @default.
- W4221156912 date "2022-02-02" @default.
- W4221156912 modified "2023-09-29" @default.
- W4221156912 title "On gluing semigroups in $mathbb{N}^n$ and the consequences" @default.
- W4221156912 doi "https://doi.org/10.48550/arxiv.2202.01189" @default.
- W4221156912 hasPublicationYear "2022" @default.
- W4221156912 type Work @default.
- W4221156912 citedByCount "0" @default.
- W4221156912 crossrefType "posted-content" @default.
- W4221156912 hasAuthorship W4221156912A5008189220 @default.
- W4221156912 hasAuthorship W4221156912A5072916907 @default.
- W4221156912 hasBestOaLocation W42211569121 @default.
- W4221156912 hasConcept C114614502 @default.
- W4221156912 hasConcept C118615104 @default.
- W4221156912 hasConcept C207405024 @default.
- W4221156912 hasConcept C2779628518 @default.
- W4221156912 hasConcept C33676613 @default.
- W4221156912 hasConcept C33923547 @default.
- W4221156912 hasConceptScore W4221156912C114614502 @default.
- W4221156912 hasConceptScore W4221156912C118615104 @default.
- W4221156912 hasConceptScore W4221156912C207405024 @default.
- W4221156912 hasConceptScore W4221156912C2779628518 @default.
- W4221156912 hasConceptScore W4221156912C33676613 @default.
- W4221156912 hasConceptScore W4221156912C33923547 @default.
- W4221156912 hasLocation W42211569121 @default.
- W4221156912 hasOpenAccess W4221156912 @default.
- W4221156912 hasPrimaryLocation W42211569121 @default.
- W4221156912 hasRelatedWork W12354402 @default.
- W4221156912 hasRelatedWork W19656136 @default.
- W4221156912 hasRelatedWork W20681527 @default.
- W4221156912 hasRelatedWork W28031397 @default.
- W4221156912 hasRelatedWork W31413193 @default.
- W4221156912 hasRelatedWork W35027071 @default.
- W4221156912 hasRelatedWork W60948150 @default.
- W4221156912 hasRelatedWork W61480950 @default.
- W4221156912 hasRelatedWork W61632769 @default.
- W4221156912 hasRelatedWork W8833220 @default.
- W4221156912 isParatext "false" @default.
- W4221156912 isRetracted "false" @default.
- W4221156912 workType "article" @default.