4 papers · 1 filter
HS-stability and complex products in involution semigroups
Bertalan Bodor, Erkko Lehtonen, Thomas Quinn-Gregson +1
When does the complex product of a given number of subsets of a group generate the same subgroup as their union? We answer this question in a more general form by introducing HS-st…
Counting finite-dimensional algebras over finite fields
Nikolaas D. Verhulst
In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed dimension over a given finite field. We show how this method works for…
Towards a Chevalley-style non-commutative algebraic geometry
Nikolaas Verhulst
We aim to construct a non-commutative algebraic geometry by using generalised valuations. To this end, we introduce groupoid valuation rings and associate suitable value functions…
Arithmetical pseudo-valuations associated to Dubrovin valuation rings and prime divisors of bounded Krull domains
Freddy Van Oystaeyen, Nikolaas Verhulst
We look at value functions of primes in simple Artinian rings and associate arithmetical pseudo-valuations to Dubrovin valuation rings which, in the Noetherian case, are $\mathbb{Z…