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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....

The algebra of the subspace semigroup of M ₂ ( q )

Jan Okniński (2002)

Colloquium Mathematicae

The semigroup S = S ( M ₂ ( q ) ) of subspaces of the algebra M ₂ ( q ) of 2 × 2 matrices over a finite field q is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.

The general structure of inverse polynomial modules

Sangwon Park (2001)

Czechoslovak Mathematical Journal

In this paper we compute injective, projective and flat dimensions of inverse polynomial modules as R [ x ] -modules. We also generalize Hom and Ext functors of inverse polynomial modules to any submonoid but we show Tor functor of inverse polynomial modules can be generalized only for a symmetric submonoid.

The Strong Anick Conjecture is true

Vesselin Drensky, Jie-Tai Yu (2007)

Journal of the European Mathematical Society

Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K 〈 x , y , z 〉 over a field K of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of K 〈 x , y , z 〉 . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a...

Currently displaying 81 – 100 of 105