1 Let B be a finite left regular band, k a commutative ring
with unit, and X,Y G A (B).
Foster, The idempotent elements of a commutative ring
form a Boolean Algebra, Duke math.
p] and R a commutative ring
with 1 (called also unital) of prime characteristic p with nil-radical N(R).
This identity holds in both the ring of integers and the ring of rational numbers, and more generally in any commutative ring
Mukesh Kumar Singh  analyzed a public key cryptosystem with matrices and the security of system depends on the difficulty of solving a system of multivariate congruence equations over a specified commutative ring
We fix a commutative ring
A and consider the category of A-weighted sets whose objects are pairs (X, f) where X is a finite set and f: X [right arrow] A is an arbitrary map called the weight of X.
Recall that the annihilator of an element r in a commutative ring
R is the collection, denoted ann(r), of elements s in R with the property that rs = 0.
Hirano, On annihilator ideals of a polynomial ring over a non commutative ring
Let K be a unital associative commutative ring
, V be a unital K-module, and [E.
In Section 2 we give the basic definitions for matroids over a commutative ring
, including representability, and we explain how they generalize the classical ones.
2](x, y)f(w) = 0 for all x, y, w [member of] R, and since R is commutative ring
with identity, so it is clear that U = where [r.
This volume contains eight chapters on the abstract algebra question of whether there is a commutative ring
with identity that has n zero-divisions.