Torsion-free modules and syzygies.
Totally indefinite Euclidean quaternion fields
We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.
Toward an arithmetic of polynomials.
Toward parametric Cohen-Macaulayfication of two-dimensional finite local cohomology domains.
Towards a theory of Bass numbers with application to Gorenstein algebras
The notion of Gorenstein rings in the commutative ring theory is generalized to that of Noetherian algebras which are not necessarily commutative. We faithfully follow in the steps of the commutative case: Gorenstein algebras will be defined using the notion of Cousin complexes developed by R. Y. Sharp [Sh1]. One of the goals of the present paper is the characterization of Gorenstein algebras in terms of Bass numbers. The commutative theory of Bass numbers turns out to carry over with no extra changes....
Towards the automated synthesis of a Gröbner bases algorithm.
We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with...
Trace Ideals of Relation Modules of Finite Groups.
Traces and differential operators over Beilinson completion algebras
Traces in strict Frobenius algebras and strict complete intersections.
Transfer of the notion of -rings to fibre products. (Transfert de la notion de -anneaux aux produits fibres.)
Transfert de Scharlau et formes quadratiques d'enlacement dans les corps de nombres
Transforms of ideals in a commutative ring.
Treillis d'idéaux et structure d'anneaux
Treuflache Äquivalenzrelationen in der Kategorie der lokal geringten Räume
Trivial formal fibres and formal Laurent series
Truncations of the ring of number-theoretic functions.
Twisted forms of finite étale extensions and separable polynomials.
Two applications of dualizing complexes over local rings
Two Examples of the Bass-Quillen-Suslin Conjectures.
Two iterative functional equations for power series.