Encyclopedia

Boolean ring

Also found in: Wikipedia.

Boolean ring

[¦bül·ē·ən ′riŋ]
(mathematics)
A commutative ring with the property that for every element a of the ring, a × a and a + a = 0; it can be shown to be equivalent to a Boolean algebra.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
Mentioned in
References in periodicals archive
Theorem.2.3 Let R be a finite Boolean ring.Then [absolute value of ([R.sup.x])] = 1.
Neutrosophic Units of Neutrosophic Rings and Fields
It follows that the proper subset A, a maximal set of B forms a Boolean ring. B is a Boolean-near-ring, whose proper subset is a Boolean-ring, then by definition, B is a SmarandacheBoolean-near-ring.
Hence A is a maximal set with uni-element and by theorem 1 and definition A, a maximal set of B forms a Boolean ring.
On some characterization of Smarandache-boolean near-ring with sub-direct sum structure
Ryabukhin, "Boolean ring," in Encyclopaedia of Mathematics, M.
Algebraic verification method for SEREs properties via Groebner bases approaches
In the literature such rings exist naturally, for instance, the rings [Z.sub.6] (modulo integers), [Z.sub.10] (modulo integers), Boolean ring.
On Smarandache rings
Copyright © 2003-2025 Farlex, Inc Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.