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For $k \in ℕ \cup {\infty}$ and $U$ open in $ℝ$ , let $C^{k} (U)$ be the ring of real valued functions on $U$ with the first $k$ derivatives continuous. It is shown that for $f \in C^{k} (U)$ there is $g \in C^{\infty} (ℝ)$ with $U \subseteq coz g$ and $h \in C^{k} (ℝ)$ with ${f g |}_{U} {= h |}_{U}$ . The function $f$ and its $k$ derivatives are not assumed to be bounded on $U$ . The function $g$ is constructed using splines based on the Mollifier function. Some consequences about the ring $C^{k} (ℝ)$ are deduced from this, in particular that $Q_{cl} (C^{k} (ℝ)) = Q (C^{k} (ℝ))$ .

On extensions of partial $x$ -operators

Ladislav Skula (1976)

Czechoslovak Mathematical Journal

On $f$ -rings that are not formally real

James J. Madden (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Henriksen and Isbell showed in 1962 that some commutative rings admit total orderings that violate equational laws (in the language of lattice-ordered rings) that are satisfied by all totally-ordered fields. In this paper, we review the work of Henriksen and Isbell on this topic, construct and classify some examples that illustrate this phenomenon using the valuation theory of Hion (in the process, answering a question posed in [E]) and, finally, prove that a base for the equational theory of totally-ordered...

On Factorization into Prime Ideals

Robert Gilmer (1972)

Commentarii mathematici Helvetici

On finite algebras projectively represented by graded complete intersections.

Günter Scheja, Uwe Storch (1993)

Mathematische Zeitschrift

On Finite Conductor Domains.

Muhammad Zafrullah (1978)

Manuscripta mathematica

On finite principal ideal rings.

Cazaran, J., Kelarev, A.V. (1999)

Acta Mathematica Universitatis Comenianae. New Series

On finitely generated birational flat extensions of integral domains

Susumu Oda (2004)

Annales mathématiques Blaise Pascal

On finitely generated multiplication ideals in commutative rings

Adil G. Naoum, Majid M. Balboul (1985)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

On finitely generated multiplication modules

R. Nekooei (2005)

Czechoslovak Mathematical Journal

We shall prove that if $M$ is a finitely generated multiplication module and $A n n (M)$ is a finitely generated ideal of $R$ , then there exists a distributive lattice $\bar{M}$ such that $S p e c (M)$ with Zariski topology is homeomorphic to $S p e c (\bar{M})$ to Stone topology. Finally we shall give a characterization of finitely generated multiplication $R$ -modules $M$ such that $A n n (M)$ is a finitely generated ideal of $R$ .

On Form Ideals and Artin-Rees Condition.

Luca Chiantini (1981)

Manuscripta mathematica

On formal groups over complete discrete valuation rings with application to a theorem of Lutz.

Keiichi Oshikawa (1982)

Journal für die reine und angewandte Mathematik

On Gaussian polynomials and content ideal.

Bakkari, Chahrazade, Mahdou, Najib (2009)

Beiträge zur Algebra und Geometrie

On generalized derivations of partially ordered sets

Ahmed Y. Abdelwanis, Abdelkarim Boua (2019)

Communications in Mathematics

Let $P$ be a poset and $d$ be a derivation on $P$ . In this research, the notion of generalized $d$ -derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized $d$ -derivations are introduced. The properties of the fixed points based on the generalized $d$ -derivations are examined. The properties of ideals and operations related with generalized $d$ -derivations are studied.

On generalized quaternion algebras.

Szeto, George (1980)

International Journal of Mathematics and Mathematical Sciences

On generalized Redei functions.

Matthews, R., Lidl, R. (1988)

International Journal of Mathematics and Mathematical Sciences

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