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Quantum sections and Gauge algebras.

Lieven Le Bruyn, Freddy van Oystaeyen (1992)

Publicacions Matemàtiques

Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates...

Skew inverse power series rings over a ring with projective socle

Kamal Paykan (2017)

Czechoslovak Mathematical Journal

A ring R is called a right PS -ring if its socle, Soc ( R R ) , is projective. Nicholson and Watters have shown that if R is a right PS -ring, then so are the polynomial ring R [ x ] and power series ring R [ [ x ] ] . In this paper, it is proved that, under suitable conditions, if R has a (flat) projective socle, then so does the skew inverse power series ring R [ [ x - 1 ; α , δ ] ] and the skew polynomial ring R [ x ; α , δ ] , where R is an associative ring equipped with an automorphism α and an α -derivation δ . Our results extend and unify many existing results....

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