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Displaying 121 – 140 of 151

Una generalizzazione di certe algebre che intervengono nella teoria dei sistemi

Maria Grazia Maia (1982)

Rendiconti del Seminario Matematico della Università di Padova

Un'algebra locale reticolata che interviene nella teoria dei sistemi

Gabriele Darbo (1978)

Rendiconti del Seminario Matematico della Università di Padova

Unique $a$ -closure for some $ℓ$ -groups of rational valued functions

Anthony W. Hager, Chawne M. Kimber, Warren W. McGovern (2005)

Czechoslovak Mathematical Journal

Usually, an abelian $ℓ$ -group, even an archimedean $ℓ$ -group, has a relatively large infinity of distinct $a$ -closures. Here, we find a reasonably large class with unique and perfectly describable $a$ -closure, the class of archimedean $ℓ$ -groups with weak unit which are “ $ℚ$ -convex”. ( $ℚ$ is the group of rationals.) Any $C (X, ℚ)$ is $ℚ$ -convex and its unique $a$ -closure is the Alexandroff algebra of functions on $X$ defined from the clopen sets; this is sometimes $C (X)$ .

Unital Embedding and Complexification of F-Algebras.

F. Beukers, C. Huijsmans, B.de Pagter (1983)

Mathematische Zeitschrift

Weakly associative lattice rings

Dana Šalounová (2000)

Acta Mathematica et Informatica Universitatis Ostraviensis

When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

A lattice-ordered ring $ℝ$ is called an OIRI-ring if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those $f$ -rings $ℝ$ such that $ℝ / 𝕀$ is contained in an $f$ -ring with an identity element that is a strong order unit for some nil $l$ -ideal $𝕀$ of $ℝ$ . In particular, if $P (ℝ)$ denotes the set of nilpotent elements of the $f$ -ring $ℝ$ , then $ℝ$ is an OIRI-ring if and only if $ℝ / P (ℝ)$ is contained in an $f$ -ring with an identity element that is a strong order unit....