Abstract
The rings of this paper are assumed to have relations of orthogonality defined on them. Such relations are uniquely determined by complete boolean algebras of ideals. Using the Stone space of these boolean algebras, and following J. Dauns and K.H. Hofmann, a sheaf-theoretic representation is obtained for rings with orthogonality relations, and the rings of global sections of these sheaves are characterized. Baer rings, f–rings and commutative semi-prime rings have natural orthogonality relations and among these the Baer rings are isomorphic to their associated rings of global sections. A special type of ideal is singled out in commutative semi-prime rings and following G. Spirason and E. Strzelecki, in an unpublished note, a characterization of a class of such rings is obtained.
Publisher
Cambridge University Press (CUP)
Reference7 articles.
1. Compact spaces of minimal prime ideals
2. The representation of biregular rings by sheaves
3. Modules over commutative regular rings;Pierce;Mem. Amer. Math. Soc.,1967
4. [6] Spirason G. and Strzelecki E. , “A note on P t -ideals” (submitted).
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Orthosystems of submodules of a module;Communications in Algebra;2023-01-11
2. Maximal perpendicularity in certain Abelian groups;Acta Universitatis Sapientiae, Mathematica;2017-08-01
3. ORTHOGONALITIES IN THE MULTIPLICATIVE GROUP Q+;Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika;2015-12-01
4. ORTHOGONALITIES IN Z p ⊕Z p;Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika;2015-08-01
5. Perpendicularity in an Abelian Group;International Journal of Mathematics and Mathematical Sciences;2013