Let be a commutative ring. By denote the Boolean algebra of idempotents of whose meet operation is given by the multiplication of . the Pierce spectrum of is the poset (in fact locale) of ideals of . There is a sheaf of indecomposable rings (rings whose only idempotents are and ) on , called the Pierce sheaf, whose ring of sections over the principal ideal (where is a prime filter in ) is .
F. Borceux, G. Janelidze, Galois Theories, Cambridge studies in advanced mathematics, 72, Cambridge University Press 2001.
P. T. Johnstone, Stone Spaces, Cambridge studies in advanced mathematics 3, Cambrdge Univ. Press 1982.