Pseudolattice properties of the star-orthogonal partial ordering for star-regular rings
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- by Robert E. Hartwig PDF
- Proc. Amer. Math. Soc. 77 (1979), 299-303 Request permission
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 $\{ c|c \geqslant a,c \geqslant b\}$ is nonempty if and only if $a \vee b$ exists in R, in which case \[ a \vee b = a + (1 - a{a^\dagger })b{b^ \ast }{[(1 - {a^\dagger }a){b^ \ast }]^\dagger }.\]References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 77 (1979), 299-303
- MSC: Primary 06F25; Secondary 15A24
- DOI: https://doi.org/10.1090/S0002-9939-1979-0545584-7
- MathSciNet review: 545584