6 papers
Generalising Latin square orthogonality and Frobenius-König with alternating sign matrices
Alena Ernst, Stefano Lia, Cian O'Brien +2
The theory of Latin squares has a long history. While the objects themselves appeared earlier, the study of their general mathematical theory dates back to Euler in the 18th centur…
On Steinberg algebras of Hausdorff ample groupoids over commutative semirings
Tran Giang Nam, Jens Zumbrägel
We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over a commutative semiring S. In particular, we obtain a complete characterization of congruence…
Designs and codes in affine geometry
Jens Zumbrägel
Classical designs and their (projective) q-analogs can both be viewed as designs in matroids, using the matroid of all subsets of a set and the matroid of linearly independent subs…
On Simpleness of Semirings and Complete Semirings
Yefim Katsov, Tran Giang Nam, Jens Zumbrägel
In this paper, among other results, there are described (complete) simple - simultaneously ideal- and congruence-simple - endomorphism semirings of (complete) idempotent commutativ…
On simple ringoids
Jens Zumbrägel
A ringoid is a set with two binary operations that are linked by the distributive laws. We study special classes of ringoids that are congruence-simple or ideal-simple. In particul…
Classification of finite congruence-simple semirings with zero
Jens Zumbrägel
Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomor…