Matches in SemOpenAlex for { <https://semopenalex.org/work/W51133760> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W51133760 abstract "This paper is motivated by an attempt to solve an old problem of Wiegand, which asks whether the projective dimension of an ideal in a commutative von Neumann regular ring depends only on the lattice of idempotents in that ideal. We compute the projective dimension of some infinitely generated ideals in von Neumann regular rings. In previous work, this projective dimension, if computable, was either ‘obvious’ or the subscript of the aleph of a generating set. We give nontrivial examples which can have arbitrary preassigned projective dimension and arbitrarily large cardinality of a generating set. The paper then presents a function l from the class of all nonzero submodules of projective modules over a von Neumann regular ring to the class of all ordinals. This function depends only on the lattice of cyclic submodules of M. We show that l (М) = 0 ⇔ M is projective and l (M) ≥ pd (M). We conjecture that pd (M) < ∞ ⇒ pd (M) = l (M) for all M. Since l (M) is defined lattice theoretically, this would answer Wiegand’s question affirmatively. Even if our conjecture is false, l (М) seems like an interesting lattice invariant to explore." @default.
- W51133760 created "2016-06-24" @default.
- W51133760 creator A5039248585 @default.
- W51133760 date "1997-01-01" @default.
- W51133760 modified "2023-09-24" @default.
- W51133760 title "Projective Dimension of Ideals in von Neumann Regular Rings" @default.
- W51133760 cites W1573797068 @default.
- W51133760 cites W1964763313 @default.
- W51133760 cites W1989909685 @default.
- W51133760 cites W2002050593 @default.
- W51133760 cites W2045735167 @default.
- W51133760 cites W2055693724 @default.
- W51133760 cites W4255550729 @default.
- W51133760 doi "https://doi.org/10.1007/978-1-4612-1978-1_21" @default.
- W51133760 hasPublicationYear "1997" @default.
- W51133760 type Work @default.
- W51133760 sameAs 51133760 @default.
- W51133760 citedByCount "1" @default.
- W51133760 crossrefType "book-chapter" @default.
- W51133760 hasAuthorship W51133760A5039248585 @default.
- W51133760 hasConcept C114614502 @default.
- W51133760 hasConcept C118615104 @default.
- W51133760 hasConcept C121332964 @default.
- W51133760 hasConcept C124101348 @default.
- W51133760 hasConcept C161491579 @default.
- W51133760 hasConcept C177846678 @default.
- W51133760 hasConcept C183778304 @default.
- W51133760 hasConcept C202444582 @default.
- W51133760 hasConcept C24890656 @default.
- W51133760 hasConcept C2780990831 @default.
- W51133760 hasConcept C2781204021 @default.
- W51133760 hasConcept C33923547 @default.
- W51133760 hasConcept C41008148 @default.
- W51133760 hasConcept C80469333 @default.
- W51133760 hasConcept C87117476 @default.
- W51133760 hasConceptScore W51133760C114614502 @default.
- W51133760 hasConceptScore W51133760C118615104 @default.
- W51133760 hasConceptScore W51133760C121332964 @default.
- W51133760 hasConceptScore W51133760C124101348 @default.
- W51133760 hasConceptScore W51133760C161491579 @default.
- W51133760 hasConceptScore W51133760C177846678 @default.
- W51133760 hasConceptScore W51133760C183778304 @default.
- W51133760 hasConceptScore W51133760C202444582 @default.
- W51133760 hasConceptScore W51133760C24890656 @default.
- W51133760 hasConceptScore W51133760C2780990831 @default.
- W51133760 hasConceptScore W51133760C2781204021 @default.
- W51133760 hasConceptScore W51133760C33923547 @default.
- W51133760 hasConceptScore W51133760C41008148 @default.
- W51133760 hasConceptScore W51133760C80469333 @default.
- W51133760 hasConceptScore W51133760C87117476 @default.
- W51133760 hasLocation W511337601 @default.
- W51133760 hasOpenAccess W51133760 @default.
- W51133760 hasPrimaryLocation W511337601 @default.
- W51133760 hasRelatedWork W1511630871 @default.
- W51133760 hasRelatedWork W1969234823 @default.
- W51133760 hasRelatedWork W1970068670 @default.
- W51133760 hasRelatedWork W1999227128 @default.
- W51133760 hasRelatedWork W2011876675 @default.
- W51133760 hasRelatedWork W2050143733 @default.
- W51133760 hasRelatedWork W2081784510 @default.
- W51133760 hasRelatedWork W2092797910 @default.
- W51133760 hasRelatedWork W2802397680 @default.
- W51133760 hasRelatedWork W2885244344 @default.
- W51133760 hasRelatedWork W2887321563 @default.
- W51133760 hasRelatedWork W2949267330 @default.
- W51133760 hasRelatedWork W2951635376 @default.
- W51133760 hasRelatedWork W2953029105 @default.
- W51133760 hasRelatedWork W2962770866 @default.
- W51133760 hasRelatedWork W2962805248 @default.
- W51133760 hasRelatedWork W2964078237 @default.
- W51133760 hasRelatedWork W3102923577 @default.
- W51133760 hasRelatedWork W3136162914 @default.
- W51133760 hasRelatedWork W3201118933 @default.
- W51133760 isParatext "false" @default.
- W51133760 isRetracted "false" @default.
- W51133760 magId "51133760" @default.
- W51133760 workType "book-chapter" @default.