36 citations · 78 across the 16 of their papers we have counts for
8 papers · 1 filter
The Extension Theorem for Bi-invariant Weights over Frobenius Rings and Frobenius Bimodules
Oliver W. Gnilke, Marcus Greferath, Thomas Honold +2
We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobe…
On congruence-semisimple semirings and the -group characterization of ultramatricial algebras over semifields
Yefim Katsov, Tran Giang Nam, Jens Zumbrägel
In this paper, we provide a complete description of congruence-semisimple semirings and introduce the pre-ordered abelian Grothendieck groups and of the isomorph…
MacWilliams' extension theorem for infinite rings
Friedrich Martin Schneider, Jens Zumbrägel
Finite Frobenius rings have been characterized as precisely those finite rings satisfying the MacWilliams extension property, by work of Wood. In the present note we offer a genera…
Every simple compact semiring is finite
Friedrich Martin Schneider, Jens Zumbrägel
A Hausdorff topological semiring is called simple if every non-zero continuous homomorphism into another Hausdorff topological semiring is injective. Classical work by Anzai and Ka…
MacWilliams' Extension Theorem for Bi-Invariant Weights over Finite Principal Ideal Rings
Marcus Greferath, Thomas Honold, Cathy Mc Fadden +2
A finite ring R and a weight w on R satisfy the Extension Property if every R-linear w-isometry between two R-linear codes in R^n extends to a monomial transformation of R^n that p…
Finite simple additively idempotent semirings
Andreas Kendziorra, Jens Zumbrägel
Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simpl…