Publication
Independence algebras, basis algebras and the distributivity condition
| dc.contributor.author | Bentz, Wolfram | |
| dc.contributor.author | Gould, Victoria | |
| dc.date.accessioned | 2023-01-30T15:32:59Z | |
| dc.date.available | 2023-01-30T15:32:59Z | |
| dc.date.issued | 2020-10-22 | |
| dc.description | Preprint de "W. Bentz and V. Gould, “Independence Algebras, Basis Algebras and the Distributivity Condition”, Acta Mathematica Hungarica 162 (2020), 419–444." | pt_PT |
| dc.description.abstract | Stable basis algebras were introduced by Fountain and Gould and developed in a series of articles. They form a class of universal algebras, extending that of independence algebras, and reflecting the way in which free modules over well-behaved domains generalise vector spaces. If a stable basis algebra B satisfies the distributivity condition (a condition satisfied by all the previously known examples), it is a reduct of an independence algebra A. Our first aim is to give an example of an independence algebra not satisfying the distributivity condition. Gould showed that if a stable basis algebra B with the distributivity condition has finite rank, then so does the independence algebra A of which it is a reduct, and that in this case the endomorphism monoid End(B) of B is a left order in the endomorphism monoid End(A) of A. We complete the picture by determining when End(B) is a right, and hence a two-sided, order in End(A). In fact (for rank at least 2), this happens precisely when every element of End(A) can be written as α]β where α, β ∈ End(B), α] is the inverse of α in a subgroup of End(A) and α and β have the same kernel. This is equivalent to End(B) being a special kind of left order in End(A) known as straight. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | Bentz, W., Gould, V. Independence algebras, basis algebras and the distributivity condition. Acta Math. Hungar. 162, 419–444 (2020). | pt_PT |
| dc.identifier.doi | 10.1007/s10474-020-01084-9 | pt_PT |
| dc.identifier.eissn | 1588-2632 | |
| dc.identifier.issn | 0236-5294 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/13253 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Springer | pt_PT |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
| dc.subject | Independence algebras | pt_PT |
| dc.subject | Basis algebras | pt_PT |
| dc.subject | V∗-algebras | pt_PT |
| dc.subject | Reduct | pt_PT |
| dc.subject | Order | pt_PT |
| dc.title | Independence algebras, basis algebras and the distributivity condition | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 440 | pt_PT |
| oaire.citation.startPage | 419 | pt_PT |
| oaire.citation.title | Acta Mathematica Hungarica | pt_PT |
| oaire.citation.volume | 162 | pt_PT |
| person.familyName | Bentz | |
| person.familyName | Gould | |
| person.givenName | Wolfram | |
| person.givenName | Victoria | |
| person.identifier.ciencia-id | BE11-F004-1168 | |
| person.identifier.orcid | 0000-0003-0002-1277 | |
| person.identifier.orcid | 0000-0001-8753-693X | |
| person.identifier.scopus-author-id | 56213213600 | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
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