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Year 2023, Volume: 34 Issue: 34, 21 - 30, 10.07.2023

Bernard Rybolowıcz

https://doi.org/10.24330/ieja.1260475
Cited By: 1

Abstract

References

  • R. Baer, Zur einfuhrung des scharbegriffs, J. Reine Angew. Math., 160 (1929),199-207.
  • M. Barr and C. Wells, Toposes, triples and theories, Corrected reprint of the 1985 original Repr. Theory Appl. Categ., 12 (2005), 1-288.
  • G. M. Bergman, An Invitation to General Algebra and Universal Constructions, Springer, Cham, Second Edition, 2015, available online, https://math.berkeley.edu/ gbergman/245/3.2.pdf.
  • T. Brzezinski, Trusses: paragons, ideals and modules, J. Pure Appl. Algebra, 224(6) (2020), 106258 (39 pp).
  • T. Brzezinski and B. Rybolowicz, Modules over trusses vs modules over rings: direct sums and free modules, Algebr. Represent. Theory, 25(1) (2022), 1-23.
  • D. S. Dummit and R. M. Foote, Abstract Algebra, Prentice Hall, 1991.
  • W. Dyck, Gruppentheoretische studien, Math. Ann., 20(1) (1882), 1-44.
  • S. Mac Lane, Categories for the Working Mathematician, Springer, New York, Second Edition, 1998.
  • H. Prufer, Theorie der abelschen gruppen, Math. Z., 20(1) (1924), 165-187.

A note on a free group. The decomposition of a free group functor through the category of heaps

Year 2023, Volume: 34 Issue: 34, 21 - 30, 10.07.2023

Bernard Rybolowıcz

https://doi.org/10.24330/ieja.1260475
Cited By: 1

Abstract

This note aims to introduce a left adjoint functor to the functor
which assigns a heap to a group. The adjunction is monadic. It is
explained how one can decompose a free group functor through the
previously introduced adjoint and employ it to describe a slightly
different construction of free groups.

Keywords

Heap free group free group functor

References

  • R. Baer, Zur einfuhrung des scharbegriffs, J. Reine Angew. Math., 160 (1929),199-207.
  • M. Barr and C. Wells, Toposes, triples and theories, Corrected reprint of the 1985 original Repr. Theory Appl. Categ., 12 (2005), 1-288.
  • G. M. Bergman, An Invitation to General Algebra and Universal Constructions, Springer, Cham, Second Edition, 2015, available online, https://math.berkeley.edu/ gbergman/245/3.2.pdf.
  • T. Brzezinski, Trusses: paragons, ideals and modules, J. Pure Appl. Algebra, 224(6) (2020), 106258 (39 pp).
  • T. Brzezinski and B. Rybolowicz, Modules over trusses vs modules over rings: direct sums and free modules, Algebr. Represent. Theory, 25(1) (2022), 1-23.
  • D. S. Dummit and R. M. Foote, Abstract Algebra, Prentice Hall, 1991.
  • W. Dyck, Gruppentheoretische studien, Math. Ann., 20(1) (1882), 1-44.
  • S. Mac Lane, Categories for the Working Mathematician, Springer, New York, Second Edition, 1998.
  • H. Prufer, Theorie der abelschen gruppen, Math. Z., 20(1) (1924), 165-187.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Bernard Rybolowıcz This is me

Early Pub Date May 11, 2023
Publication Date July 10, 2023
Published in Issue Year 2023 Volume: 34 Issue: 34

Cite

APA Rybolowıcz, B. (2023). A note on a free group. The decomposition of a free group functor through the category of heaps. International Electronic Journal of Algebra, 34(34), 21-30. https://doi.org/10.24330/ieja.1260475
AMA Rybolowıcz B. A note on a free group. The decomposition of a free group functor through the category of heaps. IEJA. July 2023;34(34):21-30. doi:10.24330/ieja.1260475
Chicago Rybolowıcz, Bernard. “A Note on a Free Group. The Decomposition of a Free Group Functor through the Category of Heaps”. International Electronic Journal of Algebra 34, no. 34 (July 2023): 21-30. https://doi.org/10.24330/ieja.1260475.
EndNote Rybolowıcz B (July 1, 2023) A note on a free group. The decomposition of a free group functor through the category of heaps. International Electronic Journal of Algebra 34 34 21–30.
IEEE B. Rybolowıcz, “A note on a free group. The decomposition of a free group functor through the category of heaps”, IEJA, vol. 34, no. 34, pp. 21–30, 2023, doi: 10.24330/ieja.1260475.
ISNAD Rybolowıcz, Bernard. “A Note on a Free Group. The Decomposition of a Free Group Functor through the Category of Heaps”. International Electronic Journal of Algebra 34/34 (July 2023), 21-30. https://doi.org/10.24330/ieja.1260475.
JAMA Rybolowıcz B. A note on a free group. The decomposition of a free group functor through the category of heaps. IEJA. 2023;34:21–30.
MLA Rybolowıcz, Bernard. “A Note on a Free Group. The Decomposition of a Free Group Functor through the Category of Heaps”. International Electronic Journal of Algebra, vol. 34, no. 34, 2023, pp. 21-30, doi:10.24330/ieja.1260475.
Vancouver Rybolowıcz B. A note on a free group. The decomposition of a free group functor through the category of heaps. IEJA. 2023;34(34):21-30.

Cited By

Heaps of modules and affine spaces
Annali di Matematica Pura ed Applicata (1923 -)
https://doi.org/10.1007/s10231-023-01369-0