On reflexive subobject lattices and reflexive endomorphism algebras

Dong Sheng Zhao

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 1, page 23-32
  • ISSN: 0010-2628

Abstract

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In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.

How to cite

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Zhao, Dong Sheng. "On reflexive subobject lattices and reflexive endomorphism algebras." Commentationes Mathematicae Universitatis Carolinae 44.1 (2003): 23-32. <http://eudml.org/doc/249147>.

@article{Zhao2003,
abstract = {In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.},
author = {Zhao, Dong Sheng},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {concrete category; optimal subset; reflexive subobject lattice; reflexive endomorphism algebra; concrete category; optimal subset; reflexive subobject lattice; reflexive endomorphism algebra},
language = {eng},
number = {1},
pages = {23-32},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On reflexive subobject lattices and reflexive endomorphism algebras},
url = {http://eudml.org/doc/249147},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Zhao, Dong Sheng
TI - On reflexive subobject lattices and reflexive endomorphism algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 1
SP - 23
EP - 32
AB - In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.
LA - eng
KW - concrete category; optimal subset; reflexive subobject lattice; reflexive endomorphism algebra; concrete category; optimal subset; reflexive subobject lattice; reflexive endomorphism algebra
UR - http://eudml.org/doc/249147
ER -

References

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  3. Halmos P.R., Reflexive lattices of subspaces, J. London Math. Soc. 4 (1971), 257-263. (1971) Zbl0231.47003MR0288612
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  6. Longstaff W.E., Strongly reflexive subspace lattices, J. London Math. Soc. (2) 11 (1975), 491-498. (1975) MR0394233
  7. Longstaff W.E., On lattices whose every realization on Hilbert space is reflexive, J. London Math. Soc. (2) 37 (1988), 499-508. (1988) Zbl0654.47025MR0939125
  8. Longstaff W.E., Oreste P., On the ranks of single elements of reflexive operator algebras, Proc. Amer. Math. Soc. 125 (10) (1997), 2875-2882. (1997) Zbl0883.47024MR1402872
  9. Manes E.G., Algebraic Theories, Graduate Texts in Mathematics 26, Springer-Verlag, 1976. Zbl0489.18003MR0419557
  10. Ore O., Structures and group theory I, Duke Math. J. 3 (1937), 149-173. (1937) Zbl0016.35103MR1545977
  11. Ore O., Structures and group theory II, Duke Math. J. 4 (1938), 247-269. (1938) Zbl0020.34801MR1546048
  12. Schmidt R., Subgroup Lattices of Groups, De Gruyter Expositions in Mathematics 14, Walter de Gruyter, Berlin-New York, 1994. Zbl1026.20015MR1292462
  13. Raney G.N., Completely distributive lattices, Proc. Amer. Math. Soc. 3 (1952), 677-680. (1952) MR0052392

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