The algebraic structure of pseudomeadow

Hamid Kulosman

Commentationes Mathematicae Universitatis Carolinae (2024)

  • Issue: 1, page 13-30
  • ISSN: 0010-2628

Abstract

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The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as the subdirect products of fields to the case of commutative pseudomeadows. Finally, we investigate localizations of commutative pseudomeadows.

How to cite

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Kulosman, Hamid. "The algebraic structure of pseudomeadow." Commentationes Mathematicae Universitatis Carolinae (2024): 13-30. <http://eudml.org/doc/299946>.

@article{Kulosman2024,
abstract = {The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as the subdirect products of fields to the case of commutative pseudomeadows. Finally, we investigate localizations of commutative pseudomeadows.},
author = {Kulosman, Hamid},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {absolutely flat ring; direct product of fields; idempotent; meadow; pseudomeadow; pseudoring; subdirect product of fields; von Neumann regular ring},
language = {eng},
number = {1},
pages = {13-30},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The algebraic structure of pseudomeadow},
url = {http://eudml.org/doc/299946},
year = {2024},
}

TY - JOUR
AU - Kulosman, Hamid
TI - The algebraic structure of pseudomeadow
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2024
PB - Charles University in Prague, Faculty of Mathematics and Physics
IS - 1
SP - 13
EP - 30
AB - The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as the subdirect products of fields to the case of commutative pseudomeadows. Finally, we investigate localizations of commutative pseudomeadows.
LA - eng
KW - absolutely flat ring; direct product of fields; idempotent; meadow; pseudomeadow; pseudoring; subdirect product of fields; von Neumann regular ring
UR - http://eudml.org/doc/299946
ER -

References

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  1. Bergstra J. A., Bethke I., Subvarieties of the variety of meadows, Sci. Ann. Comput. Sci. 27 (2017), no. 1, 1–18. MR3798461
  2. Bethke I., Rodenburg P., Sevenster A., 10.1016/j.jlamp.2014.08.004, J. Log. Algebr. Methods Program. 84 (2015), no. 2, 276–282. MR3310420DOI10.1016/j.jlamp.2014.08.004
  3. Birkhoff G., 10.1090/S0002-9904-1944-08235-9, Bull. Amer. Math. Soc. 50 (1944), 764–768. MR0010542DOI10.1090/S0002-9904-1944-08235-9
  4. Bourbaki N., Elements of Mathematics. Commutative Algebra, Hermann, Paris; Addison-Wesley Publishing, Reading, 1972. MR0360549
  5. McCoy N. H., 10.1215/S0012-7094-38-00441-7, Duke Math. J. 4 (1938), no. 3, 486–494. MR1546070DOI10.1215/S0012-7094-38-00441-7
  6. Goodearl K. R., Von Neumann Regular Rings, Monographs and Studies in Mathematics, 4, Pitman, Boston, Mass.-London, 1979. Zbl0841.16008MR0533669
  7. Kaplansky I., Commutative Rings, University of Chicago Press, Chicago, London, 1974. Zbl0296.13001MR0345945
  8. Köthe G., 10.1007/BF01455710, Math. Ann. 103 (1930), no. 1, 545–572. MR1512637DOI10.1007/BF01455710
  9. Kulosman H., Review MR3310420 for Mathematical Reviews for the paper “The structure of finite meadows", by I. Bethke, P. Rodenburg, A. Sevenster, J. Log. Algebr. Methods Program. 84 (2015), no. 2, 276–282. MR3310420
  10. Kunz E., Introduction to Commutative Algebra and Algebraic Geometry, Birkhäuser, Boston, 1985. Zbl0563.13001MR0789602
  11. von Neumann J., 10.1073/pnas.22.12.707, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 707–713. DOI10.1073/pnas.22.12.707
  12. Olivier J.-P., Anneaux absolument plats universels et épimorphismes à buts réduits, Séminaire Samuel. Algèbre commutative 2 (1967/68), exp. no. 6, 1–12 (French). MR0238836

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