UNIVERSITY OF HERTFORDSHIRE
COMPUTER SCIENCE RESEARCH COLLOQUIUM
presents
"Prime Decomposition Theorem for Finite Idempotent Semirings
using the Triangular Product of B. I. Plotkin"
Prof. John L. Rhodes
(Mathematics Department, University of California,
Berkeley, U.S.A.)
10 April 2008 (THURSDAY)
Wright Building, Room F326
Hatfield, College Lane Campus
4 - 5+ pm
Coffee/tea and biscuits will be available.
Everyone is Welcome to Attend
Abstract:
A Prime Decomposition Theorem for finite idempotent semirings is
proved using the triangular product of Plotkin adapted to
semirings. A pair of results referred to as the Triangular
Decomposition Theorem and the Ideal Decomposition Theorem are
presented. Applying these in the context of idempotent semirings
yields the decomposition half of the Prime Decomposition Theorem for
idempotent semirings. Further portions of the talk are devoted to
proving matrix algebras over the power set of a finite group are
irreducible with respect to the triangular product.
A moral of the talk is that much more of ring theory works over
semirings than one would except. Applications to computing group
complexity of the power set of a finite semigroup are given.
This is new joint research with Ben Steinberg and is covered in Chapter
9 of our recent book 'The q-theory of Finite Semigroups' Springer
2008. The talk will be adapted to a computer science audience.
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Hertfordshire Computer Science Research Colloquium
http://homepages.feis.herts.ac.uk/~nehaniv/colloq