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| Titel: |
Perfect GMV-Algebras |
| Auteur: |
Nola, A. Di Dvurecenskij, A. Tsinakis, C. |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 36 (2008) nr. 4 pagina's 1221-1249 |
| Jaar: |
2008-04 |
| Inhoud: |
The focus of this article is the class of perfect GMV-algebras, which includes all noncommutative analogs of perfect MV-algebras. As in the commutative case, we show that each perfect GMV-algebra possesses a single negation, it is generated by its infinitesimal elements, and can be uniquely realized as an interval in a lexicographical product of the lattice-ordered group of integers and an arbitrary lattice-ordered group. Further, we establish that the category of perfect GMV-algebras is equivalent to the category of all lattice-ordered groups. The variety of GMV-algebras generated by the class of perfect GMV-algebras plays a key role in our considerations. Among other results, we describe a finite equational basis for this variety and prove that it fails to satisfy the amalgamation property. In fact, we show that uncountably many of its subvarieties fail this property. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 26 van 32 gevonden artikelen
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