Medial subcartesian products of fields
Minimal degree solutions for the Bezout equation
Minimal degree solutions of polynomial equations
Minimale Erzeugendenanzahl von Moduln.
Modules quadratiques
Modulo canonico di anelli ridotti di dimensione uno e semigruppi loro associati. t-successioni
Multiplicities and Hilbert Functions under Blowing Up.
Nicht-ausgeartete reguläre Überlagerungen.
Noether's problem over an algebraically closed field.
Non-existence of the Artin function for Henselian pairs.
Normal bases for infinite Galois ring extensions
Normality of monomial ideals in two sets of variables.
Note on strongly nil clean elements in rings
Let be an associative unital ring and let be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.
Note on the transitivity of pure essential extensions
Notes on generalizations of Bézout rings
In this paper, we give new characterizations of the --Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non--Bézout --Bézout rings and examples of non--Bézout --Bézout rings.
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 Retract of an Integral Domain.
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 approximate roots of a polynomial.