Boolean algebra is also important in many other branches of methematics.
George Boole(1815-1864) introduced an important class of algebraic structures in connection with his research in methematical logic. These structures have been called Boolean a...
Boolean algebra is also important in many other branches of methematics.
George Boole(1815-1864) introduced an important class of algebraic structures in connection with his research in methematical logic. These structures have been called Boolean algebras.
These are a special type of lattice. It was E. Schroder, who about 1890, considered the lattice concept in today's sense. At approximately the same time, R. dedikind developed a similar concept in his work on groups and ideals.
In this note, we first recall the basic structures and properties of Boolean algebra by lattice, next compare Boolean algebra with Boolean ring.
There is a close connection between Boolean algebra and particular commutative rings with unit, the so-called Boolean rings. For an outline of this, we consider one more operation on Boolean algebra definable in terms of +, ·and -, symmetric deference.