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Atoms in lattice of radical classes of lattice-ordered groups

Dao Rong Tong (1993)

Archivum Mathematicum

There are several special kinds of radical classes. For example, a product radical class is closed under forming product, a closed-kernel radical class is closed under taking order closures, a K -radical class is closed under taking K -isomorphic images, a polar kernel radical class is closed under taking double polars, etc. The set of all radical classes of the same kind is a complete lattice. In this paper we discuss atoms in these lattices. We prove that every nontrivial element in these lattices...

Autour des groupes cycliquement ordonnés

G. Leloup (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Ce travail commence par rappeler les définitions et les résultats de base concernant les groupes cycliquement ordonnés, et mentionner différents domaines où ils apparaissent. Ensuite sont exposés quelques développements, notamment sur la théorie du premier ordre, les séries formelles à exposants dans un groupe cycliquement ordonné, les groupes valués dont la valuation est à valeurs dans un ensemble cycliquement ordonné, et un analogue pour les espaces ultramétriques.

Banaschewski’s theorem for generalized M V -algebras

Ján Jakubík (2007)

Czechoslovak Mathematical Journal

A generalized M V -algebra 𝒜 is called representable if it is a subdirect product of linearly ordered generalized M V -algebras. Let S be the system of all congruence relations ρ on 𝒜 such that the quotient algebra 𝒜 / ρ is representable. In the present paper we prove that the system S has a least element.

Cantor extension of a half lineary cyclically ordered group

Štefan Černák (2001)

Discussiones Mathematicae - General Algebra and Applications

Convergent and fundamental sequences are studied in a half linearly cyclically ordered group G with the abelian increasing part. The main result is the construction of the Cantor extension of G.

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