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Transitive closures of binary relations and relations α with the property that any two α-sequences connecting two given elements are of the same length are investigated. Vyšetřují se tranzitivní uzávěry binárních relací a relací α s vlast-ností, ˇ ze každé dvě α-posloupnosti spojující dané dva prvky mají stejnou délku. The present short note collects a few… (More)
Transitive closures of the covering relation in semilattices are investigated. Vyšetřují se tranzitivní uzávěry pokr´yvací relace v polosvazech. This very short note is an immediate continuation of . We therefore refer to  as for terminology, notation, various remarks, further references, etc. 1. The covering relation in semilattices Throughout the… (More)
Transitive closures of the covering relation in lattices are investigated. Vyšetřují se tranzitivní uzávěry pokr´yvací relace ve svazech. This extremely short expository note collects a few more or less notoriously known results on the covering relation β in lattices. Special attention is paid to the property that any two β-sequences connecting two given… (More)
The existence of congruence-simple semiring S with non-constant multiplication such that 2s = 3t for all s, t ∈ S and S + S = S is proved and hence the most enigmatic class of congruence-simple semirings is not empty.