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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Pseudolattice properties of the star-orthogonal partial ordering for star-regular rings


Author: Robert E. Hartwig
Journal: Proc. Amer. Math. Soc. 77 (1979), 299-303
MSC: Primary 06F25; Secondary 15A24
MathSciNet review: 545584
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Abstract: It is shown that a star-regular ring R forms a pseudo upper semilattice under the star-orthogonal partial ordering. That is, for every a, b in R, the set $ \{ c\vert c \geqslant a,c \geqslant b\} $ is nonempty if and only if $ a \vee b$ exists in R, in which case

$\displaystyle a \vee b = a + (1 - a{a^\dag })b{b^ \ast }{[(1 - {a^\dag }a){b^ \ast }]^\dag }.$


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DOI: https://doi.org/10.1090/S0002-9939-1979-0545584-7
Article copyright: © Copyright 1979 American Mathematical Society