Idempotent semigroups and tropical algebraic sets

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

The tropical semifield, i.e., the real numbers enhanced by the operations of addition and maximum, serves as a base of tropical mathematics. Addition is an abelian group operation, whereas the maximum defines an idempotent semigroup structure. We address the question of the geometry of idempotent semigroups, in particular, tropical algebraic sets carrying the structure of a commutative idempotent semigroup. We show that commutative idempotent semigroups are contractible, that systems of tropical polynomials, formed from univariate monomials, define subsemigroups with respect to coordinatewise tropical addition (maximum); and, finally, we prove that the subsemigroups in Rn which are either tropical hypersurfaces, or tropical curves in the plane or in the three-space have the above polynomial description.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)489-520
عدد الصفحات32
دوريةJournal of the European Mathematical Society
مستوى الصوت14
رقم الإصدار2
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 2012

All Science Journal Classification (ASJC) codes

  • !!Applied Mathematics
  • !!General Mathematics

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