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This work discusses the problem of Arens regularity of a lattice-ordered ring. In this prospect, a counterexample is furnished to show that without extra conditions, a lattice-ordered ring need not be Arens regular. However, as shown in this paper, it turns out that any $f$ -ring in the sense of Birkhoff and Pierce is Arens regular. This result is then used and extended to the more general setting of almost $f$ -rings introduced again by Birkhoff.

Characterization of fuzzy neighborhood commutative division rings. II.

Ahsanullah, T.M.G., Al-Thukair, Fawzi A. (1995)

International Journal of Mathematics and Mathematical Sciences

Charakerisierung der lokalbeschränkten Ringtopologien auf globalen Körpern.

Hans Weber (1979)

Mathematische Annalen

Closed normal subgroups in groups of units of compact rings.

Tripe, Adela (2003)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Coalgebras, comodules, pseudocompact algebras and tame comodule type

Daniel Simson (2001)

Colloquium Mathematicae

We develop a technique for the study of K-coalgebras and their representation types by applying a quiver technique and topologically pseudocompact modules over pseudocompact K-algebras in the sense of Gabriel [17], [19]. A definition of tame comodule type and wild comodule type for K-coalgebras over an algebraically closed field K is introduced. Tame and wild coalgebras are studied by means of their finite-dimensional subcoalgebras. A weak version of the tame-wild dichotomy theorem of Drozd [13]...

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A characterization of discrete linearly compact rings by means of a duality

A characterization of fuzzy neighborhood commutative division rings.

A characterization of Linearly Compact Modules.

A decomposition theorem for complete comodule algebras over complete Hopf algebras

A Generalisation of Swan's Theorem.

Abelian groups whose endomorphism ring is linearly compact

Approximation durch Polynomfunktionen auf universellen Algebren.

Archimedean property of ordered semirings.

Arens regularity of lattice-ordered rings

Characterization of fuzzy neighborhood commutative division rings. II.

Charakerisierung der lokalbeschränkten Ringtopologien auf globalen Körpern.

Closed normal subgroups in groups of units of compact rings.

Coalgebras, comodules, pseudocompact algebras and tame comodule type

Compact Rings.

Completions of Regular Rings.

Continuity of characters in products of algebras

Die Struktur einer Klasse linear kompakter Ringe

Dualities over compact rings

Duality and Completions of Linearly Topologized Modules.

Embeddings into Power Series Rings.

Currently displaying 1 – 20 of 150