We prove the existence of standard bases and unique remainder for ideals in power series rings with respect to arbitrary admissible term order. Several characterizations of standard bases are shown to be equivalent. We give an algorithm that computes the unique remainder of a power series modulo a principal ideal with respect to the lexicographical term order. The algorithm applies to the Weierstrass preparation theorem
In this paper a new notion of reduction depending on an arbitrary non-empty set ORD of term ordering...
A constructive proof is given of the termination of the algorithm for computing standard bases in po...
The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to p...
We prove the existence of standard bases and unique remainder for ideals in power series rings with ...
AbstractWe show that w.r.t. fixed admissible term order, every ideal in a ring of power series over ...
AbstractWe show that w.r.t. fixed admissible term order, every ideal in a ring of power series over ...
We investigate the behavior of standard bases (in the sense of Hironaka and Grauert) for ideals in r...
This article presents the standard bases for ideals, in the context of formal power series rings ove...
AbstractIfKis a field, let the ringR′consist of finite sums of homogeneous elements inR=K[[x1,x2,x3,...
When is an ideal of a ring radical or prime? By examining its generators, one may in many cases defi...
When is an ideal of a ring radical or prime? By examining its generators, one may in many cases defi...
If K is a field, let the ring R ′ consist of finite sums of homogeneous elements in R = K[[x1,x2,x3,...
AbstractThe author defines canonical bases for ideals in polynomial rings over Z and develops an alg...
Using recent work by Erman–Sam–Snowden, we show that finitely generated ideals in the ring of bounde...
AbstractIn this paper we study standard bases for submodules of K[[t1,…,tm]][x1,…,xn]s respectively ...
In this paper a new notion of reduction depending on an arbitrary non-empty set ORD of term ordering...
A constructive proof is given of the termination of the algorithm for computing standard bases in po...
The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to p...
We prove the existence of standard bases and unique remainder for ideals in power series rings with ...
AbstractWe show that w.r.t. fixed admissible term order, every ideal in a ring of power series over ...
AbstractWe show that w.r.t. fixed admissible term order, every ideal in a ring of power series over ...
We investigate the behavior of standard bases (in the sense of Hironaka and Grauert) for ideals in r...
This article presents the standard bases for ideals, in the context of formal power series rings ove...
AbstractIfKis a field, let the ringR′consist of finite sums of homogeneous elements inR=K[[x1,x2,x3,...
When is an ideal of a ring radical or prime? By examining its generators, one may in many cases defi...
When is an ideal of a ring radical or prime? By examining its generators, one may in many cases defi...
If K is a field, let the ring R ′ consist of finite sums of homogeneous elements in R = K[[x1,x2,x3,...
AbstractThe author defines canonical bases for ideals in polynomial rings over Z and develops an alg...
Using recent work by Erman–Sam–Snowden, we show that finitely generated ideals in the ring of bounde...
AbstractIn this paper we study standard bases for submodules of K[[t1,…,tm]][x1,…,xn]s respectively ...
In this paper a new notion of reduction depending on an arbitrary non-empty set ORD of term ordering...
A constructive proof is given of the termination of the algorithm for computing standard bases in po...
The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to p...
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