On a formula of Beniamino Segre.
On a functional equation arising from hyperbolic geometry.
On a generalization of a Prüfer-Kaplansky-Procházka theorem
On a generalization of de Rham lemma
Let be a free module over a noetherian ring. For , let be the ideal generated by coefficients of . For an element with , if , there exists such that .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.
On a homology of algebras with unit
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 -Kasch spaces
If is a Tychonoff space, its ring of real-valued continuous functions. In this paper, we study non-essential ideals in . Let be a infinite cardinal, then is called -Kasch (resp. -Kasch) space if given any ideal (resp. -ideal) with then is a non-essential ideal. We show that is an -Kasch space if and only if is an almost -space and is an -Kasch space if and only if is a pseudocompact and almost -space. Let denote the socle of . For a topological space with only...
On a lifting problem for principal Dedekind domains
On a non-vanishing Ext
On a notion of “Galois closure” for extensions of rings
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 degree 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
On a result of avramov.
On a Retract of an Integral Domain.
On a Special Class of Non Complete Webs
In this article, we introduce a special class of non complete webs, the NN-webs. We also study the algebraic and geometric properties of these webs.
On a theorem by Kronecker.
On a theorem of F. S. Macaulay on colon ideals.
On a theorem of Fröberg and saturated graphs.
On abelian separable extensions and Galois sets of rings
On algebraic closures.
This is a description of some different approaches which have been taken to the problem of generalizing the algebraic closure of a field. Work surveyed is by Enoch and Hochster (commutative algebra), Raphael (categories and rings of quotients), Borho (the polynomial approach), and Carson (logic).Later work and applications are given.
On Almost Complete Intersections.