Some remarks on structural matrix rings and matrices with ideal entries

Details Some remarks on structural matrix rings and matrices with ideal entries Some remarks on structural matrix rings and matrices with ideal entries

2010-12-08

arxiv.org/abs/1012.1887v2

Miskolc Mathematical Notes 12 (2011) 25-29

Mathematics

Rings and Algebras

Corrections, added references

Scientific paper

Associating to each pre-order on the indices 1,...,n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n x n matrix rings. Rings within the order-convex hull of the embedding, i.e. matrix rings that contain the ring of diagonal matrices, can be viewed as incidence algebras of ideal-valued, generalized pre-order relations. Certain conjugates of the upper or lower triangular matrix rings correspond to the various linear orderings of the indices, and the incidence algebras of partial orderings arise as intersections of such conjugate matrix rings.

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