In this paper, we generalize the notion of an implicativity discussed in B C K -algebras, and apply it to some groupoids and B C K -algebras. We obtain some relations among those axioms in the theory of groupoids.
In this paper, we introduce the notion of a BV-algebra, and we show that a BV-algebra is logically equivalent to several algebras, i.e., BM-algebras, BT-algebras, BO-algebras and 0-commutative B-algebras. Moreover, we show that a BV-algebra with (F) is logically equivalent to several algebras, and we show some relationships between a BV-algebra with (F) and several related algebras.
Abstract. Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 6-dimensional Einstein's connection in terms of the unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in 6-dimensional Einstein's unified field theory (i.e., 6-g-UFT):I. The recurrence relations in 6-g-UFT. II. The Einstein's connection in 6-g-UFT.All considerations in these papers are restricted to the first and second classes only, since the case of the third class, the simplest case, was already studied by many authors.
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