Gröbner bases of modules
Skew PBW Extensions: Ring and Module-theoretic Properties, Matrix and Gröbner …, 2020•Springer
Gröbner Bases of Modules Page 1 Chapter 14 Gröbner Bases of Modules In this chapter we
construct the general theory of Gröbner bases for submodules of Am, m ≥ 1, where A = σ(R)〈x1,...,xn〉
is a bijective skew PBW extension of R, with R a LGS ring (see Definition 13.2.1) and Mon(A)
endowed with some monomial order (see Definition 13.1.1). This theory was studied in [191]
and [192], but now we will extend Buchberger’s algorithm to the general bijective case
without assuming that A is quasi-commutative. Am is the left free A-module of column vectors …
construct the general theory of Gröbner bases for submodules of Am, m ≥ 1, where A = σ(R)〈x1,...,xn〉
is a bijective skew PBW extension of R, with R a LGS ring (see Definition 13.2.1) and Mon(A)
endowed with some monomial order (see Definition 13.1.1). This theory was studied in [191]
and [192], but now we will extend Buchberger’s algorithm to the general bijective case
without assuming that A is quasi-commutative. Am is the left free A-module of column vectors …
Abstract
The results presented in this chapter are an easy generalization of those of the previous chapter, i.e., taking m = 1 we get the theory of Gröbner bases for the left ideals of A.
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