Let be a poset and be a derivation on . In this research, the notion of generalized -derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized -derivations are introduced. The properties of the fixed points based on the generalized -derivations are examined. The properties of ideals and operations related with generalized -derivations are studied.
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.
We study unitary rings of characteristic 2 satisfying identity for some natural number p. We characterize several infinite families of these rings which are Boolean, i.e., every element is idempotent. For example, it is in the case if or or for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form or where q is a natural number and .
It is well known that to every Boolean ring can be assigned a Boolean algebra whose operations are term operations of . Then a symmetric difference of together with the meet operation recover the original ring operations of . The aim of this paper is to show for what a ring a similar construction is possible. Of course, we do not construct a Boolean algebra but only so-called lattice-like structure which was introduced and treated by the authors in a previous paper. In particular, we reached...
De Morgan quasirings are connected to De Morgan algebras in the same way as Boolean rings are connected to Boolean algebras. The aim of the paper is to establish a common axiom system for both De Morgan quasirings and De Morgan algebras and to show how an interval of a De Morgan algebra (or De Morgan quasiring) can be viewed as a De Morgan algebra (or De Morgan quasiring, respectively).
The notion of L-fuzzy extended ideals is introduced in a Boolean ring, and their essential properties are investigated. We also build the relation between an L-fuzzy ideal and the class of its L-fuzzy extended ideals. By defining an operator “⇝” between two arbitrary L-fuzzy ideals in terms of L-fuzzy extended ideals, the result that “the family of all L-fuzzy ideals in a Boolean ring is a complete Heyting algebra” is immediately obtained. Furthermore, the lattice structures of L-fuzzy extended...