The injective hull of an archimedean f-algebra

A. W. Wickstead

Compositio Mathematica (1987)

  • Volume: 62, Issue: 3, page 329-342
  • ISSN: 0010-437X

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Wickstead, A. W.. "The injective hull of an archimedean f-algebra." Compositio Mathematica 62.3 (1987): 329-342. <http://eudml.org/doc/89844>.

@article{Wickstead1987,
author = {Wickstead, A. W.},
journal = {Compositio Mathematica},
keywords = {extended orthomorphism; Archimedean Riesz space; weak orthomorphism; order dense ideal; semiprime Archimedean f-algebra; von Neumann regular f-algebra; self-injective; laterally complete; injective hull},
language = {eng},
number = {3},
pages = {329-342},
publisher = {Martinus Nijhoff Publishers},
title = {The injective hull of an archimedean f-algebra},
url = {http://eudml.org/doc/89844},
volume = {62},
year = {1987},
}

TY - JOUR
AU - Wickstead, A. W.
TI - The injective hull of an archimedean f-algebra
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 62
IS - 3
SP - 329
EP - 342
LA - eng
KW - extended orthomorphism; Archimedean Riesz space; weak orthomorphism; order dense ideal; semiprime Archimedean f-algebra; von Neumann regular f-algebra; self-injective; laterally complete; injective hull
UR - http://eudml.org/doc/89844
ER -

References

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  2. 2 S.J. Bernau: Lateral and Dedekind completion of Archimedean lattice groups. J. London Math. Soc. (2) 12 (1976) 320-322. Zbl0333.06008MR401579
  3. 3 F. Beukers, C.B. Huismans and B. de Pagter: Unital Embedding and Complexification of F-algebras. Math. Z.183 (1983) 131-144. Zbl0494.06010MR701362
  4. 4 A. Bigard and K. Keimel: Les orthomorphismes d'un espace reticule Archimedien. Indag. Math.34 (1972) 236-246. Zbl0235.06008MR308000
  5. 5 P.F. Conrad and J.E. Diem: The ring of polar preserving endomorphisms of an abelian lattice ordered group. Illinois J. Math.15 (1971) 224-240. Zbl0213.04002MR285462
  6. 6 M. Duhoux and M. Meyer: A new proof of the lattice structure of orthomorphisms. J. London Math. Soc. (2) 25 (1982) 375-378. Zbl0485.46002MR653395
  7. 7 M. Duhoux and M. Meyer: Extended orthomorphisms on Archimedean Riesz spaces. Ann. Mat. pura et appl. (IV) 33 (1983) 193-226. Zbl0526.46010MR725026
  8. 8 M. Duhoux and M. Meyer: Extended orthomorphisms and lateral completion of Archimedean Riesz spaces. Ann. Soc. Sci. Bruxelles98 (1984) 3-18. Zbl0559.46003MR766282
  9. 9 M. Duhoux and M. Meyer: Extension and inversion of extended orthomorphisms on Riesz spaces. J. Austral. Math. Soc.37 (1984) 223-242. Zbl0559.46002MR749502
  10. 10 C. Faith: Algebra II, Ring Theory. Springer-Verlag, Berlin - Heidelberg - New York (1976). Zbl0335.16002MR427349
  11. 11 M. Henriksen: Semiprime ideals in f-rings. Symposia Math.21 (1977) 401-409. Zbl0374.06013MR480256
  12. 12 C.B. Huijsmans and B. de Pagter: Ideal theory in f-algebras. Trans. Amer. Math. Soc.269 (1982) 225-245. Zbl0483.06009MR637036
  13. 13 C.B. Huijsmans and B. de Pagter: The order bidual of lattice ordered algebras. J. Functional Anal.59 (1984) 41-64. Zbl0549.46006MR763776
  14. 14 J. Lambek: Lectures on rings and modules. Blaisdell, Waltham, Massachusetts - Toronto - London (1966). Zbl0143.26403MR206032
  15. 15 W.A.J. Luxemburg and L.C. Moore Jr.: Archimedean Quotient Riesz spaces. Duke Math. J.34 (1967) 725-739. Zbl0171.10501MR217562
  16. 16 W.A.J. Luxemburg and A.R. Schep: A Radon-Nikodym type theorem for positive operators and a dual. Indag. Math.40 (1978) 357-375. Zbl0389.47018MR507829
  17. 17 W.A.J. Luxemburg and A.C. Zaanen: Riesz Spaces I. North-Holland, Amsterdam - London (1971). Zbl0231.46014MR511676
  18. 18 B. de Pagter: The space of extended orthomorphisms in a Riesz space. Pacific J. Math.112 (1984) 193-210. Zbl0541.46006MR739146
  19. 19 A.W. Wickstead: Representation and duality of multiplication operators on Archimedean Riesz spaces. Compositio Math.35 (1977) 225-238. Zbl0381.47021MR454728
  20. 20 A.W. Wickstead: Extensions of orthomorphisms. J. Austral. Math. Soc.29 (1980) 87-98. Zbl0435.47040MR566279

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