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The main theorem characterizes, in terms of bracket powers, an- alytic spread one ideals in local rings. Specically, let b1;:::;bg;xbe regular nonunits in a local (Noetherian) ring (R;M) and assume that I (xR)a ,t he integral closure of xR ,w hereI =( b1;:::;bg;x)R. Then the main result shows that for all but nitely many units u1;:::;ug in R that are non-congruent modulo M and for all large integers n and k it holds that Ijn = I(j)n for j =1 ;:::;kand j not divisible by char(R=M), where I(j) is the j-th bracket power ((b1 +u1x)j;:::;(bg +ugx)j;xj)R of I =( b1 +u1x;:::;bg +ugx;x)R. And, conversely, if there exist positive integers g, n ,a ndk n+g g such that I has a basis 1;:::;g;xsuch that Ikn =( 1k;:::;gk;xk)nR ,t henI has analytic spread one.

A bracket power characterization of analytic spread one ideals