Orthogonal Completions of Reduced Rings with Respect to Abian Order
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 477-489
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In this paper, it is proved that a reduced ring R has an orthogonal completion if and only if for every idempotent e e R, eR has an orthogonal completion. Every orthogonal subset X of R has a supremum in Q max(R), the maximal two sided ring of quotients of R, and the orthogonal completion of a reduced ring R, if it exists, is isomorphic to a unique subring of Q max(R). Hence the orthogonal completion of a reduced ring R, if it exists, is unique upto isomorphism. A reduced ring R has an orthogonal completion if and only if the collection of those elements of Q max(R) which are supremums of orthogonal subsets of R form a subring of Q max(R). Furthermore, every projectable ring R has an orthogonal completion , which is a Baer ring. It is also proved that for projectable rings R, where is the idempotent filter of those dense right ideals of R which contain a maximal orthogonal subset of idempotents of R.
Rai, R. K. Orthogonal Completions of Reduced Rings with Respect to Abian Order. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 477-489. doi: 10.4153/CMB-1980-073-2
@article{10_4153_CMB_1980_073_2,
author = {Rai, R. K.},
title = {Orthogonal {Completions} of {Reduced} {Rings} with {Respect} to {Abian} {Order}},
journal = {Canadian mathematical bulletin},
pages = {477--489},
year = {1980},
volume = {23},
number = {4},
doi = {10.4153/CMB-1980-073-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-073-2/}
}
TY - JOUR AU - Rai, R. K. TI - Orthogonal Completions of Reduced Rings with Respect to Abian Order JO - Canadian mathematical bulletin PY - 1980 SP - 477 EP - 489 VL - 23 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-073-2/ DO - 10.4153/CMB-1980-073-2 ID - 10_4153_CMB_1980_073_2 ER -
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