Titlebook: Algorithmic Methods in Non-Commutative Algebra; Applications to Quan José Bueso,José Gómez-Torrecillas,Alain Verschoren Book 2003 Springer

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Hippocampus

,Gröbner basis computation algorithms, the notion of admissible order ℕ. and show how this may be used to define left Poincaré-Birkhoff-Witt (PBW) rings. The elements of these rings exhibit a behaviour which is similar to that of ordinary, commutative polynomials, allowing them to be approached computationally. Left PBW rings are actual

Heart-Attack

First applications,ce many of these applications are non-commutative analogs of corresponding ones in the commutative case, our presentation runs along the lines of that in “classical” texts, like [.], for example. In this way, the reader may easily compare the commutative and the non-commutative approach.

品尝你的人

,Gröbner bases for modules,rship or equality problem. In the present chapter we will generalize this approach and show how it applies as well to submodules of the free module ..Actually, it appears that this set-up may also be used to calculate syzygy modules, both in the ideal and (more generally) the module case. The introd

grotto

Syzygies and applications,n techniques. However, it appears that this approach is highly inefficient from the computational point of view, mainly due to the necessary use of the lex ordering (or, more generally, any elimination ordering). Actually, lots of effort has been spent in the past in order to avoid the use of elimin

CLASP

The Gelfand-Kirillov dimension and the Hilbert polynomial,otion is defined by using chains of (two-sided) prime ideals, it only makes sense for rings having “many” two-sided ideals. Fortunately, for finitely generated k-algebras ., we may define the so-called Gelfand-Kirillov dimension GKdim(.), which is a far better invariant and which, moreover, coincide

从容

陈腐思想

AVERT

Generalities on rings, book. We did, of course, not aim at a complete or self-contained exposition, as this would fall outside of the framework of the present text. Instead we restrict ourselves exactly to those topics, definitions and properties, which play a major role throughout the sequel.

含沙射影

First applications,ce many of these applications are non-commutative analogs of corresponding ones in the commutative case, our presentation runs along the lines of that in “classical” texts, like [.], for example. In this way, the reader may easily compare the commutative and the non-commutative approach.