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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....

Some counter-examples in the theory of the Galois module structure of wild extensions

Stephen M. J. Wilson (1980)

Annales de l'institut Fourier

Considering the ring of integers in a number field as a Z Γ -module (where Γ is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.

Some examples of nil Lie algebras

Ivan P. Shestakov, Efim Zelmanov (2008)

Journal of the European Mathematical Society

Generalizing Petrogradsky’s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand–Kirillov dimension over any field of positive characteristic.

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