On inverse categories with split idempotents

Emil Schwab; Emil Daniel Schwab

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 1, page 13-25
  • ISSN: 0044-8753

Abstract

top
We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators.

How to cite

top

Schwab, Emil, and Schwab, Emil Daniel. "On inverse categories with split idempotents." Archivum Mathematicum 051.1 (2015): 13-25. <http://eudml.org/doc/270036>.

@article{Schwab2015,
abstract = {We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators.},
author = {Schwab, Emil, Schwab, Emil Daniel},
journal = {Archivum Mathematicum},
keywords = {inverse categories; inverse monoids; split idempotents; pointed sets; annihilators; exact sequences},
language = {eng},
number = {1},
pages = {13-25},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On inverse categories with split idempotents},
url = {http://eudml.org/doc/270036},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Schwab, Emil
AU - Schwab, Emil Daniel
TI - On inverse categories with split idempotents
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 1
SP - 13
EP - 25
AB - We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators.
LA - eng
KW - inverse categories; inverse monoids; split idempotents; pointed sets; annihilators; exact sequences
UR - http://eudml.org/doc/270036
ER -

References

top
  1. Clifford, A.H., 10.2307/2372503, Amer. J. Math. 75 (1953), 547–556. (1953) Zbl0051.01302MR0056597DOI10.2307/2372503
  2. Jones, D.G., Lawson, M.V., 10.1016/j.jalgebra.2014.04.001, J. Algebra 409 (2014), 444–473. (2014) MR3198850DOI10.1016/j.jalgebra.2014.04.001
  3. Kastl, J., Inverse categories, Studien zur Algebra und ihre Anwendungen, Akademie-Verlag Berlin, 1979, BAnd 7, pp. 51–60. (1979) Zbl0427.18003MR0569574
  4. Kawahara, Y., 10.2206/kyushumfs.27.149, Mem. Kyushu University, Series A, Math. 27 (1973), 149–173. (1973) Zbl0261.18005MR0390017DOI10.2206/kyushumfs.27.149
  5. Leech, J., 10.1007/BF02575008, Semigroup Forum 36 (1987), 89–116. (1987) Zbl0634.18002MR0902733DOI10.1007/BF02575008
  6. Mitchell, B., Theory of categories, Acad. Press New York, 1965. (1965) Zbl0136.00604MR0202787
  7. Schwab, E., Image and inverse image mappings in exact inverse categories, Boll. U.M.I. 18–B (1981), 831–845. (1981) Zbl0477.18002MR0641740
  8. Schwab, E., Schwab, E.D., 10.1007/s11083-011-9211-7, Order 296 (2012), 405–417. (2012) MR2979640DOI10.1007/s11083-011-9211-7
  9. Schwab, E.D., Stoianov, G., 10.1216/RMJ-2011-41-5-1701, Rocky Mountain J. Math 41 (2011), 1701–1710. (2011) Zbl1233.20055MR2838084DOI10.1216/RMJ-2011-41-5-1701

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.