Boolean Algebra Structure on Sigma(S)
by
Chuang Peng
Department of Mathematics, Morehouse College, Atlanta, GA

Let S be an arbitary subset in an Abelian group G, \Sigma₀(S)=\Sigma(S) \cup {0} and \Sigma(S)={\Sigmaa_ik|  a_ik in S}. Estimating \Sigma(S) has played a very important role in the study of additive group theory. This paper defines a Boolean structure on \Sigma(S) and establishes some properties based this Boolean algebra structure. It applies the Boolean structure in the study of the conjectures on Z_p that d(Z\subp)=\lceil(\surd{8p+1}-1)/2 \rceil and c(Z\subp) = \lceil2\surd{p-1} \rceil-1, where p is prime, and d(G), c(G) are the minimum sizes of subsets which add to identity or entire group G respectively.

Date received: March 31, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caky-98.