Matches in SemOpenAlex for { <https://semopenalex.org/work/W2972422066> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2972422066 endingPage "35" @default.
- W2972422066 startingPage "1" @default.
- W2972422066 abstract "Let $H$ be a multiplicatively written monoid. Given $kin{bf N}^+$, we denote by $mathscr U_k$ the set of all $ellin{bf N}^+$ such that $a_1cdots a_k=b_1cdots b_ell$ for some atoms $a_1,ldots,a_k,b_1,ldots,b_ellin H$. The sets $mathscr U_k$ are one of the most fundamental invariants studied in the theory of non-unique factorization, and understanding their structure is a basic problem in the field: In particular, it is known that, in many cases of interest, these sets are almost arithmetic progressions with the same difference and bound for all large $k$, namely, $H$ satisfies the Structure Theorem for Unions. The present paper improves the current state of the art on this problem. More precisely, we show that, under mild assumptions on $H$, not only does the Structure Theorem for Unions hold, but there also exists $muin{bf N}^+$ such that, for every $Min{bf N}$, the sequences $$ bigl((mathscr U_k-infmathscr U_k)cap[![0,M]!]bigr)_{kge 1} quadtext{and}quad bigl((supmathscr U_k-mathscr U_k)cap[![0,M]!]bigr)_{kge 1} $$ are $mu$-periodic from some point on. The result applies, e.g., to (the multiplicative monoid of) all commutative Krull domains (e.g., Dedekind domains) with finite class group; a variety of weakly Krull commutative domains (including all orders in number fields with finite elasticity); some maximal orders in central simple algebras over global fields; and all numerical monoids. Large parts of the proofs are worked out in a purely additive model, by inquiring into the properties of what we call a subadditive family, i.e., a collection $mathscr L$ of subsets of $bf N$ such that, for all $L_1,L_2inmathscr L$, there is $Linmathscr L$ with $L_1+L_2subseteq L$." @default.
- W2972422066 created "2019-09-19" @default.
- W2972422066 creator A5069180712 @default.
- W2972422066 date "2019-09-09" @default.
- W2972422066 modified "2023-10-10" @default.
- W2972422066 title "Structural properties of subadditive families with applications to factorization theory" @default.
- W2972422066 cites W1415576118 @default.
- W2972422066 cites W1574833721 @default.
- W2972422066 cites W2029720185 @default.
- W2972422066 cites W2059858975 @default.
- W2972422066 cites W2062486464 @default.
- W2972422066 cites W2080496329 @default.
- W2972422066 cites W2080753152 @default.
- W2972422066 cites W2144161970 @default.
- W2972422066 cites W2177178416 @default.
- W2972422066 cites W2586008757 @default.
- W2972422066 cites W2641823494 @default.
- W2972422066 cites W2962761840 @default.
- W2972422066 cites W2962843469 @default.
- W2972422066 cites W2962996290 @default.
- W2972422066 cites W2964150103 @default.
- W2972422066 cites W3103884926 @default.
- W2972422066 cites W4298722907 @default.
- W2972422066 doi "https://doi.org/10.1007/s11856-019-1922-2" @default.
- W2972422066 hasPublicationYear "2019" @default.
- W2972422066 type Work @default.
- W2972422066 sameAs 2972422066 @default.
- W2972422066 citedByCount "14" @default.
- W2972422066 countsByYear W29724220662019 @default.
- W2972422066 countsByYear W29724220662020 @default.
- W2972422066 countsByYear W29724220662021 @default.
- W2972422066 countsByYear W29724220662022 @default.
- W2972422066 countsByYear W29724220662023 @default.
- W2972422066 crossrefType "journal-article" @default.
- W2972422066 hasAuthorship W2972422066A5069180712 @default.
- W2972422066 hasBestOaLocation W29724220662 @default.
- W2972422066 hasConcept C11413529 @default.
- W2972422066 hasConcept C114614502 @default.
- W2972422066 hasConcept C118615104 @default.
- W2972422066 hasConcept C134306372 @default.
- W2972422066 hasConcept C183778304 @default.
- W2972422066 hasConcept C187834632 @default.
- W2972422066 hasConcept C206901836 @default.
- W2972422066 hasConcept C33923547 @default.
- W2972422066 hasConcept C42747912 @default.
- W2972422066 hasConceptScore W2972422066C11413529 @default.
- W2972422066 hasConceptScore W2972422066C114614502 @default.
- W2972422066 hasConceptScore W2972422066C118615104 @default.
- W2972422066 hasConceptScore W2972422066C134306372 @default.
- W2972422066 hasConceptScore W2972422066C183778304 @default.
- W2972422066 hasConceptScore W2972422066C187834632 @default.
- W2972422066 hasConceptScore W2972422066C206901836 @default.
- W2972422066 hasConceptScore W2972422066C33923547 @default.
- W2972422066 hasConceptScore W2972422066C42747912 @default.
- W2972422066 hasIssue "1" @default.
- W2972422066 hasLocation W29724220661 @default.
- W2972422066 hasLocation W29724220662 @default.
- W2972422066 hasOpenAccess W2972422066 @default.
- W2972422066 hasPrimaryLocation W29724220661 @default.
- W2972422066 hasRelatedWork W1568633953 @default.
- W2972422066 hasRelatedWork W2120366296 @default.
- W2972422066 hasRelatedWork W2386248435 @default.
- W2972422066 hasRelatedWork W2544600950 @default.
- W2972422066 hasRelatedWork W2783152233 @default.
- W2972422066 hasRelatedWork W2950820214 @default.
- W2972422066 hasRelatedWork W3130993066 @default.
- W2972422066 hasRelatedWork W3161268522 @default.
- W2972422066 hasRelatedWork W4205186527 @default.
- W2972422066 hasRelatedWork W4318195686 @default.
- W2972422066 hasVolume "234" @default.
- W2972422066 isParatext "false" @default.
- W2972422066 isRetracted "false" @default.
- W2972422066 magId "2972422066" @default.
- W2972422066 workType "article" @default.