Functors <img width="72" height="53" src="http://article.sciencepublishinggroup.com/journal/347/3471098/image001.png" />, <img width="165" height="53" src="http://article.sciencepublishinggroup.com/journal/347/3471098/image002.png" />, <img width="103" height="53" src="http://article.sciencepublishinggroup.com/journal/347/3471098/image003.png" /> and <img width="146" height="53" src="http://article.sciencepublishinggroup.com/journal/347/3471098/image004.png" />in the Category of <i>A - Alg</i>

Moussa Thiaw; Mohamed Ben Faraj Ben Maaouia; Mamadou Sanghare

doi:doi:10.11648/j.ijtam.20190501.11

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Functors , , and in the Category of A - Alg

Moussa Thiaw, Mohamed Ben Faraj Ben Maaouia, Mamadou Sanghare

Received: 18 February 2019 Accepted: 26 March 2019 Published: 18 April 2019

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Abstract

The purpose of this paper is to study some results of homological algebra in the category A-Alg (resp. Alg-A) of left (resp. right) A-algebra in the noncommutative case. In this paper A is a subring of B. So the main results of this paper are, if B is a noetherian duo-ring, S a central saturated multiplicatively closed subset of A, S_R the set of regular elements of S, a finitely presented right A-algebra and a (B-A)-bialgebra, then is isomorphic to , also is isomorphic to , for any integer n.

DOI	10.11648/j.ijtam.20190501.11
Published in	International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 1, February 2019)
Page(s)	1-9
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Algebra, Multiplicatively Closed Subset, Ore Condition of Multiplicatively Closed Subset, Localized, Category, Functor, Complex Projective Resolution

References

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[2]	M. F. Atiyah and I.G.Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, University of Oxford.
[3]	H. Cartan and Samuel Eilenberg, Homological Agebra, Princeton University Press, New Jersey, 1956.
[4]	F. Dennis, Noncommutative algebra, GTM Vol.144, Springer-Verlag, 1993.
[5]	M. P. Eelbert, Localisation in Duo-ring, Kansas.Ciry, Missouri.
[6]	M. F. Maaouia and al, Functor S^-1 () and Adjoint Isomorphism, International Mathematical Forum, vol. 11, 2016, no. 5, 227-237.
[7]	N. Jacobson, Structure of rings, Amer.Math.Soc.Colloquium Publications, Vol.37, 1956.
[8]	D. M. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294-329.
[9]	Lam, A First Course in Noncommutative Rings, GTM Vol.131, Springer-Verlag, 2001.
[10]	M. F. Maaouia and al., Localization in a Duo-Ring and Polynomials Algebra, Springer International Publishing Switzerland 2016 C.T. Gueye, M.S. Molina (eds.), Non-Associative and Non-Commutative Algebra and Operator Theory, Springer Proceedings in Mathematics and Statistics 160, DOI 10.1007 978-3-319-32902-4-13.
[11]	M. F. Maaouia, Thèse d’état, Faculté des Sciences et Techniques, UCAD, Dakar, Juillet, 2011.
[12]	M. F. Maaouia, Doctorat 3ème Cycle, Faculté des Sciences et Techniques, UCAD, Dakar, Juillet, 2003.
[13]	M. F. Maaouia and M.Sanghare, Localisation Dans Les Duo-Anneaux, Afrika Mathematika, 2009.
[14]	M. F. Maaouia and M.Sanghare, Module de fraction- Sous-modules S-saturée et foncteur S^-1, International Journal of Algebra, 16(2012), 0973-1768.
[15]	M. F. Maaouia and M.Sanghare, Anneau de valuation non nécessairement commutatif et duo-anneau de Dideking, Global Journal of Pure and Applied Mathematics, ISSN 0973-1768 Volume 8, Number 1(2012).
[16]	H. Matsumura, Commutative algebra, W.A. Benjamin, New-York, 1970.
[17]	R. Pierce, Associative Algebras, Grad.Text in Math.88, Springer, 1982.
[18]	J. Rotman, Notes on Homological Algebra, University of Illinois, Urbane, 1968.
[19]	J. Rotman, An introduction to Homological Algebra, GSM Vol.114, Academic Press, New York 1972.

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APA Style

Moussa Thiaw, Mohamed Ben Faraj Ben Maaouia, Mamadou Sanghare. (2019). Functors , , and in the Category of A - Alg. International Journal of Theoretical and Applied Mathematics, 5(1), 1-9. https://doi.org/10.11648/j.ijtam.20190501.11

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ACS Style

Moussa Thiaw; Mohamed Ben Faraj Ben Maaouia; Mamadou Sanghare. Functors , , and in the Category of A - Alg. Int. J. Theor. Appl. Math. 2019, 5(1), 1-9. doi: 10.11648/j.ijtam.20190501.11

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AMA Style

Moussa Thiaw, Mohamed Ben Faraj Ben Maaouia, Mamadou Sanghare. Functors , , and in the Category of A - Alg. Int J Theor Appl Math. 2019;5(1):1-9. doi: 10.11648/j.ijtam.20190501.11

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@article{10.11648/j.ijtam.20190501.11,
  author = {Moussa Thiaw and Mohamed Ben Faraj Ben Maaouia and Mamadou Sanghare},
  title = {Functors , ,  and in the Category of A - Alg},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {5},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ijtam.20190501.11},
  url = {https://doi.org/10.11648/j.ijtam.20190501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190501.11},
  abstract = {The purpose of this paper is to study some results of homological algebra in the category A-Alg (resp. Alg-A) of left (resp. right) A-algebra in the noncommutative case. In this paper A is a subring of B. So the main results of this paper are, if B is a noetherian duo-ring, S a central saturated multiplicatively closed subset of A, SR the set of regular elements of S,  a finitely presented right A-algebra and  a (B-A)-bialgebra, then  is isomorphic to , also  is isomorphic to , for any integer n.},
 year = {2019}
}

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TY  - JOUR
T1  - Functors , ,  and in the Category of A - Alg
AU  - Moussa Thiaw
AU  - Mohamed Ben Faraj Ben Maaouia
AU  - Mamadou Sanghare
Y1  - 2019/04/18
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20190501.11
DO  - 10.11648/j.ijtam.20190501.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20190501.11
AB  - The purpose of this paper is to study some results of homological algebra in the category A-Alg (resp. Alg-A) of left (resp. right) A-algebra in the noncommutative case. In this paper A is a subring of B. So the main results of this paper are, if B is a noetherian duo-ring, S a central saturated multiplicatively closed subset of A, SR the set of regular elements of S,  a finitely presented right A-algebra and  a (B-A)-bialgebra, then  is isomorphic to , also  is isomorphic to , for any integer n.
VL  - 5
IS  - 1
ER  -

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Author Information

Moussa Thiaw

UFR of Applied Sciences and Technology, Gaston Berger University, Saint-Louis, Senegal
Mohamed Ben Faraj Ben Maaouia

UFR of Applied Sciences and Technology, Gaston Berger University, Saint-Louis, Senegal
Mamadou Sanghare

Department of Mathematics, Faculty of Science and Technology, Cheikh Anta Diop University, Dakar, Senegal

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APA Style

Moussa Thiaw, Mohamed Ben Faraj Ben Maaouia, Mamadou Sanghare. (2019). Functors , , and in the Category of A - Alg. International Journal of Theoretical and Applied Mathematics, 5(1), 1-9. https://doi.org/10.11648/j.ijtam.20190501.11

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ACS Style

Moussa Thiaw; Mohamed Ben Faraj Ben Maaouia; Mamadou Sanghare. Functors , , and in the Category of A - Alg. Int. J. Theor. Appl. Math. 2019, 5(1), 1-9. doi: 10.11648/j.ijtam.20190501.11

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AMA Style

Moussa Thiaw, Mohamed Ben Faraj Ben Maaouia, Mamadou Sanghare. Functors , , and in the Category of A - Alg. Int J Theor Appl Math. 2019;5(1):1-9. doi: 10.11648/j.ijtam.20190501.11

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@article{10.11648/j.ijtam.20190501.11,
  author = {Moussa Thiaw and Mohamed Ben Faraj Ben Maaouia and Mamadou Sanghare},
  title = {Functors , ,  and in the Category of A - Alg},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {5},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ijtam.20190501.11},
  url = {https://doi.org/10.11648/j.ijtam.20190501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190501.11},
  abstract = {The purpose of this paper is to study some results of homological algebra in the category A-Alg (resp. Alg-A) of left (resp. right) A-algebra in the noncommutative case. In this paper A is a subring of B. So the main results of this paper are, if B is a noetherian duo-ring, S a central saturated multiplicatively closed subset of A, SR the set of regular elements of S,  a finitely presented right A-algebra and  a (B-A)-bialgebra, then  is isomorphic to , also  is isomorphic to , for any integer n.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Functors , ,  and in the Category of A - Alg
AU  - Moussa Thiaw
AU  - Mohamed Ben Faraj Ben Maaouia
AU  - Mamadou Sanghare
Y1  - 2019/04/18
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20190501.11
DO  - 10.11648/j.ijtam.20190501.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20190501.11
AB  - The purpose of this paper is to study some results of homological algebra in the category A-Alg (resp. Alg-A) of left (resp. right) A-algebra in the noncommutative case. In this paper A is a subring of B. So the main results of this paper are, if B is a noetherian duo-ring, S a central saturated multiplicatively closed subset of A, SR the set of regular elements of S,  a finitely presented right A-algebra and  a (B-A)-bialgebra, then  is isomorphic to , also  is isomorphic to , for any integer n.
VL  - 5
IS  - 1
ER  -

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