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One consequence of the recent push to develop a scheme theory in tropical geometry has been the development of a tropical commutative algebra. This starts with the commutative algebra of semirings, but in order to get a theory that interacts with geometry, we are lead to impose some combinatorial, matroid-theoretic, conditions. I will introduce these ideas, and discuss the current state of our understanding.

Notes 156 KB application/pdf

Tropical Ideals