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Keleş H.

Journal of Applied and Pure Mathematics, vol.5, no.1, pp.1-8, 2023 (Peer-Reviewed Journal)


This study is on a Boolean B or Boolean lattice L in abstract
algebra with closed binary operation ∗, complement and distributive prop-
erties. Both Binary operations and logic properties dominate this set. A
lattice sheds light on binary operations and other algebraic structures. In
particular, the construction of the elements of this L set from idempotent
elements, our definition of k-order idempotent has led to the expanded def-
inition of the definition of the lattice theory. In addition, a lattice offers
clever solutions to vital problems in life with the concept of logic. The re-
striction on a lattice is clearly also limit such applications. The flexibility
of logical theories adds even more vitality to practices. This is the main
theme of the study. Therefore, the properties of the set elements resulting
from the binary operation force the logic theory. According to the new def-
inition given, some properties, lemmas and theorems of the lattice theory
are examined. Examples of different situations are given.