S. A. Badaev, S. S. Goncharov, “Rogers Semilattices of Families of Arithmetic Sets”, Algebra Logika, 2001, Volume 40, Number 5,Pages <nobr>507

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Rogers Semilattices of Families of Arithmetic Sets

S. A. Badaev^a, S. S. Goncharov^b

^a Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We look into algebraic properties of Rogers semilattices of arithmetic sets, such as the existence of minimal elements, minimal covers, and ideals without minimal elements.

Keywords: Rogers semilattice, arithmetic set, minimal element, minimal cover, and ideal.

UDC: 510.5

Received: 11.10.2000