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On The Equivalence of Categories of A^H-Semimodules and A#H-Semimodules
M. Devendran1 , V. Selvan2
Section:Research Paper, Product Type: Journal-Paper
Vol.6 ,
Issue.6 , pp.79-86, Dec-2019
Online published on Dec 31, 2019
Copyright © M. Devendran, V. Selvan . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: M. Devendran, V. Selvan, “On The Equivalence of Categories of A^H-Semimodules and A#H-Semimodules,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.79-86, 2019.
MLA Style Citation: M. Devendran, V. Selvan "On The Equivalence of Categories of A^H-Semimodules and A#H-Semimodules." International Journal of Scientific Research in Mathematical and Statistical Sciences 6.6 (2019): 79-86.
APA Style Citation: M. Devendran, V. Selvan, (2019). On The Equivalence of Categories of A^H-Semimodules and A#H-Semimodules. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(6), 79-86.
BibTex Style Citation:
@article{Devendran_2019,
author = {M. Devendran, V. Selvan},
title = {On The Equivalence of Categories of A^H-Semimodules and A#H-Semimodules},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {12 2019},
volume = {6},
Issue = {6},
month = {12},
year = {2019},
issn = {2347-2693},
pages = {79-86},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1630},
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1630
TI - On The Equivalence of Categories of A^H-Semimodules and A#H-Semimodules
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - M. Devendran, V. Selvan
PY - 2019
DA - 2019/12/31
PB - IJCSE, Indore, INDIA
SP - 79-86
IS - 6
VL - 6
SN - 2347-2693
ER -
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Abstract :
In this paper, we have introduced two functors between the category of A^H- semimodules and the category of A#H- semimodules, where A is a H-semimodule semialgebra over a Hopf algebra. Further, assuming H as a finite dimensional semisimple Hopf algebra we have established a categorical equivalence between these two categories.
Key-Words / Index Term :
Semialgebra, Smash product, Hopf algebra, Natural transformation, equivalent categories
References :
[1] Miriam Cohen and Davida Fishman, Hopf Algebra Actions, Journal of Algebra, 100, 363-379(1986).
[2] M.Devendran, V.Selvan, Hopf Algebra Actions on Semialgebras, Journal of combinatorics, information and system sciences Vol.42(2017), No.1-2, 33-50.
[3] Jonathan S Golan, Semiring and their Applications, Kluwer Academic Publishers, 1999.
[4] Saunders Maclane, Categories for working mathematicians, Graduate text in mathematics, Springer, 1971.
[5] Y.Katsov, Tensor products and injective envelopes of semimodules over additively regular semirings, Algebra Colloquium 4(2)(1997)121-131.
[6] V.Selvan, M.Devendran, Morita equivalence between H-fixed semialgebra and smash product semialgebra, Journal of combinatorics, information and system sciences, Vol.43 (2018), No.1-4, pages 57-77.
[7] R.P.Sharma, Anu, N.Singh, Partial group action on semialgebras, Asian-Eur.J.Math. 5(4)2012, Act1250060, 20pp.
[8] M.Sweedler, Hopf Algebra, Benjamin, New York, 1969.
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