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Let $M$ be a free module over a noetherian ring. For $ω_{1}, ..., ω_{k} \in M$ , let $𝒜$ be the ideal generated by coefficients of $ω_{1} \land ... \land ω_{k}$ . For an element $ω \in ⋀^{p} M$ with $p < prof . 𝒜$ , if $ω \land ω_{1} \land ... \land ω_{k} = 0$ , there exists $η_{1}, ..., η_{k} \in ⋀^{p - 1} M$ such that $ω = \sum_{i = 1}^{k} η_{i} \land ω_{i}$ .This is a generalization of a lemma on the division of forms due to de Rham (Comment. Math. Helv., 28 (1954)) and has some applications to the study of singularities.

On a Geometric Interpretation of Multiplicity.

C.P. Ramanujam (1973)

Inventiones mathematicae

On a homology of algebras with unit

Jacek Dębecki (2014)

Annales Polonici Mathematici

We present a very general construction of a chain complex for an arbitrary (even non-associative and non-commutative) algebra with unit and with any topology over a field with a suitable topology. We prove that for the algebra of smooth functions on a smooth manifold with the weak topology the homology vector spaces of this chain complex coincide with the classical singular homology groups of the manifold with real coefficients. We also show that for an associative and commutative algebra with unit...

On $a$ -Kasch spaces

Ali Akbar Estaji, Melvin Henriksen (2010)

Archivum Mathematicum

If $X$ is a Tychonoff space, $C (X)$ its ring of real-valued continuous functions. In this paper, we study non-essential ideals in $C (X)$ . Let $a$ be a infinite cardinal, then $X$ is called $a$ -Kasch (resp. $\bar{a}$ -Kasch) space if given any ideal (resp. $z$ -ideal) $I$ with $gen (I) < a$ then $I$ is a non-essential ideal. We show that $X$ is an $ℵ_{0}$ -Kasch space if and only if $X$ is an almost $P$ -space and $X$ is an $ℵ_{1}$ -Kasch space if and only if $X$ is a pseudocompact and almost $P$ -space. Let $C_{F} (X)$ denote the socle of $C (X)$ . For a topological space $X$ with only...

On a lifting problem for principal Dedekind domains

Paolo Valabrega (1974)

Rendiconti del Seminario Matematico della Università di Padova

On a non-vanishing Ext

Laszlo Fuchs, Saharon Shelah (2003)

Rendiconti del Seminario Matematico della Università di Padova

On a notion of “Galois closure” for extensions of rings

Manjul Bhargava, Matthew Satriano (2014)

Journal of the European Mathematical Society

We introduce a notion of “Galois closure” for extensions of rings. We show that the notion agrees with the usual notion of Galois closure in the case of an $S_{n}$ degree $n$ extension of fields. Moreover, we prove a number of properties of this construction; for example, we show that it is functorial and respects base change. We also investigate the behavior of this Galois closure construction for various natural classes of ring extensions.

On A Problem Of Samuel

Raj K. Markanda, Joaquin Pascual (1981)

Revista colombiana de matematicas

On a result of avramov.

Antonio G. Rodicio (1988)

Manuscripta mathematica

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