Jednoduché polookruhy

• Main Author: Kala, Vítězslav
• Other Authors: El Bashir, Robert
• Format: Dissertation
• Language: English
• Published: 2009
• Online Access: http://www.nusl.cz/ntk/nusl-275275

A well-known statement says that if a commutative field is finitely generated as a ring, then it is finite. This thesis studies a generalization of this statement - problem, whether every finitely generated ideal-simple commutative semiring is additively idempotent or finite. Using the characterization of idealsimple semirings we prove that this question is equivalent to the question, whether every commutative parasemifield (i.e., a semiring whose multiplicative semigroup is a group), which is finitely generated as a semiring, is additively idempotent. In the thesis we deduce various useful properties of such parasemifields and use them to solve the problem in the one-generated case. Finally, we mention a way of using obtained properties of parasemifields for the solution of the two-generated case via the study of subsemigroups of Nm0.