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Formations of lattice ordered groups and of $GMV$-algebras

In: Mathematica Slovaca, vol. 58, no. 5
Ján Jakubík
Detaily:
Rok, strany: 2008, 521 - 534
Kľúčové slová:
lattice ordered group, $GMV$-algebra, formation, torsion class
O článku:
A class of lattice ordered groups is called a formation if it is closed with respect to homomorphic images and finite subdirect products. Analogously we define the formation of $GMV$-algebras. Let us denote by $\cc F1$ and $\cc F2$ the collection of all formations of lattice ordered groups or of $GMV$-algebras, respectively. Both $\cc F1$ and $\cc F2$ are partially ordered by the class-theoretical inclusion. We prove that $\cc F1$ satisfies the infinite distributivity law $X\wedge \smash[b]{\bigveei\in I Xi=\bigveei\in I} (X\wedge Xi)$ and that $\cc F2$ is isomorphic to a principal ideal of $\cc F1$.
Ako citovať:
ISO 690:
Jakubík, J. 2008. Formations of lattice ordered groups and of $GMV$-algebras. In Mathematica Slovaca, vol. 58, no.5, pp. 521-534. 0139-9918.

APA:
Jakubík, J. (2008). Formations of lattice ordered groups and of $GMV$-algebras. Mathematica Slovaca, 58(5), 521-534. 0139-9918.