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- Title
Equivalence between Varieties of Łukasiewicz–Moisil Algebras and Rings.
- Authors
Martinolich, Blanca Fernanda López; Vannicola, María del Carmen
- Abstract
The Post, axled and Łukasiewicz–Moisil algebras are important lattices studied in algebraic logic. In this paper, we investigate a useful interpretation between these algebras and some rings. We give a term equivalence between Post algebras of order |$p$| and |$p$| -rings, |$p$| prime and lift this result to the axled Łukasiewicz–Moisil algebra |$L \cong B_s \times P$| and the ring |$\prod ^s F_2 \times \prod ^l F_p$| , where |$B_s$| is a Boolean algebra of order |$2^s$| , |$P$| a |$p$| -valued Post algebra of order |$p^l$| and |$F_p$| is the prime field of order |$p$|.
- Subjects
RING theory; VARIETIES (Universal algebra); ALGEBRAIC varieties; ALGEBRAIC logic; ALGEBRA; BOOLEAN algebra
- Publication
Logic Journal of the IGPL, 2023, Vol 31, Issue 5, p988
- ISSN
1367-0751
- Publication type
Article
- DOI
10.1093/jigpal/jzac061