Linear Equations over Noncommutative Graded Rings
نویسنده
چکیده
We call a graded connected algebra R effectively coherent, if for every linear equation over R with homogeneous coefficients of degrees at most d, the degrees of generators of its module of solutions are bounded by some function D(d). For commutative polynomial rings, this property has been established by Hermann in 1926. We establish the same property for several classes of noncommutative algebras, including the most common class of rings in noncommutative projective geometry, that is, strongly Noetherian rings, which includes Noetherian PI algebras and Sklyanin algebras. We extensively study so–called universally coherent algebras, that is, such that the function D(d) is bounded by 2d for d >> 0. For example, finitely presented monomial algebras belong to this class, as well as many algebras with finite Groebner basis of relations.
منابع مشابه
Proposed Research
I was a graduate student at the Mas-sachusetts Institute of Technology. The rst three years of these studies were supported by an NSF Graduate Student Fellowship. My research there led to a Ph.D. thesis entitled \Noncommutative ruled surfaces." My thesis research describes certain classes of graded rings which arise as homogeneous coordinate rings of noncommutative quantizations of algebraicall...
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