A1 - Chwastyk, Anna
N2 - In 1966 E. Marczewski introduced a general notion of independence, which contained as special cases the majority of independence notions used in various branches of mathematics - independence with respect to a family Q of mappings in an abstract algebra (Q-independence).
N2 - We investigated Q-independent subsets for some specified families Q of mappings (e.g. M, S, M, S, S 0 , A 1 , G, I ) in Stone algebras, using the triple representation of Stone algebras. Next, some of these results were generalized for algebras which have a retraction in their set of term operations. We characterized also the families of Q-independence sets in distributive lattices and semillattices for Q= S, S 0 , G and I. A special class of groupoids with involution, the so-called * -associative groupoids, was introduced. We gave the description of term operations in these algebras and investigated their Q-independent subsets.
KW - Q-niezależność
KW - algebra Stone'a
KW - retrakcja
T1 - Pojęcia niezależności w algebrach z działaniami co najwyżej dwuargumentowymi