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On duality between order and algebraic structures in Boolean systems

Dadej A., Halik K.

Journal of Mathematics and Applications

2013

Vol. 36

35--62

We present an extension of the known one-to-one correspondence between Boolean algebras and Boolean rings with unit being two types of Boolean systems endowed with order and algebraic structures, respectively. Two equivalent generalizations of Boolean algebras are discussed. We show that there is a one-to-one correspondence between any of the two mentioned generalized Boolean algebras and Boolean rings without unit.

Properties of differences in B-rings

Dadej A., Halik K.

Journal of Mathematics and Applications

2011

Vol. 34

5-13

Motivated by Pettis' extensions of Sierpinski theorems on generated families of sets, we consider B-rings, a generalization of the notion of Boolean algebras, and present their various properties. In particular, we discuss properties of differences which will be used in the proofs of results given in our forthcoming papers.