Boolean Rings

2009 ◽  
pp. 1-7
Author(s):  
Steven Givant
Keyword(s):  
Boolean Rings

Prime Ideals of Subrings of Boolean Rings

1972 ◽  
Vol s2-5 (2) ◽  
pp. 219-221
Author(s):  
Alexander Abian
Keyword(s):  
Prime Ideals ◽  
Boolean Rings

scholarly journals Extensions of Boolean Rings and Nearrings

2019 ◽  
Vol 12 (1) ◽  
pp. 58-67 ◽  
Author(s):  
Nayak Hamsa ◽  
◽  
Kuncham Syam P. ◽  
Kedukodi Babushri S. ◽  
◽  
...  
Keyword(s):  
Boolean Rings

scholarly journals Postulate-sets for Boolean rings

1944 ◽  
Vol 55 ◽  
pp. 393-393 ◽  
Author(s):  
B. A. Bernstein
Keyword(s):  
Boolean Rings

Boolean Near-Rings

1969 ◽  
Vol 12 (3) ◽  
pp. 265-273 ◽  
Author(s):  
James R. Clay ◽  
Donald A. Lawver
Keyword(s):  
Vector Space ◽  
Maximal Ideal ◽  
Boolean Ring ◽  
Affine Transformations ◽  
Isomorphism Classes ◽  
Boolean Rings ◽  
Lattice Of Ideals ◽  
Unique Maximal Ideal

In this paper we introduce the concept of Boolean near-rings. Using any Boolean ring with identity, we construct a class of Boolean near-rings, called special, and determine left ideals, ideals, factor near-rings which are Boolean rings, isomorphism classes, and ideals which are near-ring direct summands for these special Boolean near-rings.Blackett [6] discusses the near-ring of affine transformations on a vector space where the near-ring has a unique maximal ideal. Gonshor [10] defines abstract affine near-rings and completely determines the lattice of ideals for these near-rings. The near-ring of differentiable transformations is seen to be simple in [7], For near-rings with geometric interpretations, see [1] or [2].

Characterizations of Three Classes of Zero-Divisor Graphs

2012 ◽  
Vol 55 (1) ◽  
pp. 127-137 ◽  
Author(s):  
John D. LaGrange
Keyword(s):  
Commutative Ring ◽  
Direct Product ◽  
Zero Divisor ◽  
Commutative Rings ◽  
Central Vertex ◽  
Integral Domains ◽  
Boolean Rings ◽  
Zero Divisor Graph ◽  
Zero Divisors

AbstractThe zero-divisor graph Γ(R) of a commutative ring R is the graph whose vertices consist of the nonzero zero-divisors of R such that distinct vertices x and y are adjacent if and only if xy = 0. In this paper, a characterization is provided for zero-divisor graphs of Boolean rings. Also, commutative rings R such that Γ(R) is isomorphic to the zero-divisor graph of a direct product of integral domains are classified, as well as those whose zero-divisor graphs are central vertex complete.

Two Elementary Generalisations of Boolean Rings

1986 ◽  
Vol 93 (2) ◽  
pp. 121 ◽  
Author(s):  
Michael O. Searcoid ◽  
Desmond MacHale
Keyword(s):  
Boolean Rings
Sign in / Sign up

Export Citation Format

Share Document