Výzkum
	Kolokvia

Semirings (a generalization of rings, where the subtraction is in general not available) are fairy basic objects (e.g. the semiring of natural numbers) and they appear naturally in many branches of mathematics and informatics. Apart of the rings, the structure of semirings is more complicated and some basic structural properties of even the most common ones are not known (e.g. the structure of subsemirings of Q⁺ - the semiring of all positive rational numbers). Classification of the simple commutative semirings (El Bashir et al, '01) motivated a series of conjectures about idempotency in finitely generated commutative semirings. We make an overview about this topic, related ideas and the current state of the conjectures.