t-Closed Pairs
Martine Picavet-L’Hermitte · 2023
Throughout this paper, rings are assumed to be commutative with unit, and ring morphisms are unitary. If A is a ring, Bool ( A ) will denote the set of idempotents of A . t-closed rings form a special class of the seminormal rings defined by R. Swan in [ 15 ]. T. Akiba’s results about seminormal pairs [ 1 ], D. F. Anderson, D. Dobbs and J. Huckaba’s results about seminormal overrings [ 2 ] and D. Dobbs and T. Ishikawa’s results about seminormal underrings [ 7 ] led us to study some families of t-closed rings built up from one or two t-closed rings.