caa a22 4500 467899525 CHVBK 20180406152813.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s00012-006-1965-1 doi (NATIONALLICENCE)springer-10.1007/s00012-006-1965-1 Martínez Jorge Department of Mathematics, University of Florida, P. O. Box 118105, 32611-8105, Gainesville, FL, USA aut Unit and kernel systems in algebraic frames [Elektronische Daten] [Jorge Martínez] Abstract.: One considers the poset of dense, coherent frame quotients of an algebraic frame with the finite intersection property, which are compact. It is shown that there is a smallest such, the frame of d-elements. However, unless the frame is already compact there is no largest such quotient. With the additional assumption of disjointification on the frame, one then studies the maximal ideal spaces of these quotients and the relationship to covers of compact spaces. Several applications are considered, with considerable attention to the frame quotients defined by extension of ideals of a commutative ring A to a ring extension; this type of frame quotient is considered both with and without an underlying lattice structure on the rings. Birkhäuser Verlag, Basel, 2006 Primary 06D22 nationallicence secondary 06F20 nationallicence 06F25 nationallicence 18B35 nationallicence algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/1(2006-01-01), 13-43 0002-5240 55:1<13 2006 55 12 https://doi.org/10.1007/s00012-006-1965-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00012-006-1965-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Martínez Jorge Department of Mathematics, University of Florida, P. O. Box 118105, 32611-8105, Gainesville, FL, USA aut NATIONALLICENCE 773 0- algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/1(2006-01-01), 13-43 0002-5240 55:1<13 2006 55 12 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer