RMC - Vol. 10 supplementary - J. McEnerney/G. Stengle

Full paper in PDF:
$%J. McEnerney and G. Stengle, The Nonreduced Order spectrum of a commutative ring, Rev. Mat. Univ. Complut. Madrid 10 (1997), supplementary, 251–275. %$

The Nonreduced Order Spectrum of a Commutative Ring

James MCENERNEY and Gilbert STENGLE

Plasma Physics Laboratory Princeton University Princeton, NJ 08543 — USA mcenerne@math.princeton.edu	Department of Mathematics Lehigh University Bethlehem PA 18015 — USA gas0@lehigh.edu

ABSTRACT

A nonreduced order of a ring $A$ is a subset a satisfying i) $a+ a < a$ , ii) $a .a < a$ , iii) $a U a= A$ (without any restriction on $- a$ and $a$ ). The purpose of this paper is to organize these objects into a topological space or spectrum, to show relations to existing concepts, to analyze some examples, and to motivate our inquiry by questions of multiplicity.

1991 Mathematics Subject Classification: 14P99, 13J25.