Higher Dimensional Compacta with Algebraically Closed Function Algebras

Higher Dimensional Trees, Algebraically

In formal language theory, James Rogers published a series of innovative papers generalising strings and trees to higher dimensions.Motivated by applications in linguistics, his goal was to smoothly extend the core theory of the formal languages of strings and trees to these higher dimensions. Rogers’ definitions focussed on a specific representation of higher dimensional trees. This paper pres...

Noetherian algebras over algebraically closed fields

Let k be an uncountable algebraically closed field and let A be a countably generated left Noetherian k-algebra. Then we show that A⊗k K is left Noetherian for any field extension K of k. We conclude that all subfields of the quotient division algebra of a countably generated left Noetherian domain over k are finitely generated extensions of k. We give examples which show that A⊗k K need not re...

Multiplicative Complexity of Commutative Group Algebras over Algebraically Closed Fields

We determine structure and multiplicative complexity of commutative group algebras over algebraically closed fields. Commutative group algebra A of dimension n over algebraically closed field is isomorphic to B, where B is a superbasic algebra of minimal rank (see [5] for definition), and t is maximal that t | n, p t. Multiplicative and bilinear complexity of A equal to 2n − t.

Pseudo Algebraically Closed Extensions

Higher-dimensional Temperley-Lieb algebras

A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced. MSC-class: 81R50 (primary), 82B20 (secondary).