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Rings of formal power series $k [[C]]$ with exponents in a cyclically ordered group $C$ were defined in [2]. Now, there exists a “valuation” on $k [[C]]$ : for every $σ$ in $k [[C]]$ and $c$ in $C$ , we let $v (c, σ)$ be the first element of the support of $σ$ which is greater than or equal to $c$ . Structures with such a valuation can be called cyclically valued rings. Others examples of cyclically valued rings are obtained by “twisting” the multiplication in $k [[C]]$ . We prove that a cyclically valued ring is a subring of a power series ring $k [[C, θ]]$ with...

Decomposition of $ℓ$ -group-valued measures

Giuseppina Barbieri, Antonietta Valente, Hans Weber (2012)

Czechoslovak Mathematical Journal

We deal with decomposition theorems for modular measures $μ : L \to G$ defined on a D-lattice with values in a Dedekind complete $ℓ$ -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete $ℓ$ -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for $ℓ$ -group-valued...

Dimension in algebraic frames

Jorge Martinez (2006)

Czechoslovak Mathematical Journal

In an algebraic frame $L$ the dimension, $dim (L)$ , is defined, as in classical ideal theory, to be the maximum of the lengths $n$ of chains of primes $p_{0} < p_{1} < \dots < p_{n}$ , if such a maximum exists, and $\infty$ otherwise. A notion of “dominance” is then defined among the compact elements of $L$ , which affords one a primefree way to compute dimension. Various subordinate dimensions are considered on a number of frame quotients of $L$ , including the frames $d L$ and $z L$ of $d$ -elements and $z$ -elements, respectively. The more concrete illustrations...

Direct factors of directed groups

Judita Lihová (1991)

Archivum Mathematicum

Direct factors of multilattice groups

Milan Kolibiar (1990)

Archivum Mathematicum

Direct factors of multilattice groups. II.

Milan Kolibiar (1992)

Archivum Mathematicum

Subgroups of a directed distributive multilattice group $G$ are characterized which are direct factors of $G$ . The main result is formulated in Theorem 2.

Direct limits of cyclically ordered groups

Ján Jakubík, Gabriela Pringerová (1994)

Czechoslovak Mathematical Journal

Direct product decomposition of $M V$ -algebras

Ján Jakubík (1994)

Czechoslovak Mathematical Journal

Direct product decompositions of directed groups

Ján Jakubík (1989)

Czechoslovak Mathematical Journal

Direct product decompositions of pseudo effect algebras

Ján Jakubík (2005)

Mathematica Slovaca

Direct product factors in GMV-algebras

Jiří Rachůnek, Dana Šalounová (2005)

Mathematica Slovaca

Direct summands and retract mappings of generalized $M V$ -algebras

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

In the present paper we deal with generalized $M V$ -algebras ( $G M V$ -algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, $G M V$ -algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of $G M V$ -algebras. The relations between $G M V$ -algebras and lattice ordered groups are essential for this investigation.

Directed convex subgroups of ordered groups

Jiří Rachůnek (1973)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

Distinguished completion of a direct product of lattice ordered groups

Ján Jakubík (2001)

Czechoslovak Mathematical Journal

The distinguished completion $E (G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $M V$ -algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group $G$ is a direct product of lattice ordered groups $G_{i}$ $(i \in ...$

Distributivität des $l$ -Untergruppenverbandes einer Verbandsgruppe

Mária Jakubíková (1975)

Matematický časopis

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