We introduce a new construction based on directed graphs. It provides a common generalization of the incidence rings and Munn semirings. Our main theorem describes all ideals of the largest possible weight in this construction. Several previous results can be obtained as corollaries to our new main theorem.
Bulletin of Mathematical Sciences and Applications (Volume 15)
A. V. Kelarev et al., "Ideals of Largest Weight in Constructions Based on Directed Graphs", Bulletin of Mathematical Sciences and Applications, Vol. 15, pp. 8-16, 2016