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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)
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.
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)