In this manuscript we insert the concept of derivations in associative PU-algebras and discuss some of its important results such that we prove that for a mapping being a (Left, Right) or (Right, Left)-derivation of an associative PU-algebra then such a mapping is one-one. If a mapping is regular then it is identity. If any element of an associative PU-algebra satisfying the criteria of identity function then such a map is identity. We also prove some useful properties for a mapping being (Left, Right)-regular derivation of an associative PU-algebra and (Right, Left)-regular derivation of an associative PU-algebra. Moreover we prove that if a mapping is regular (Left, Right)-derivation of an associative PU-algebra then its Kernel is a subalgebra. We have no doubt that the research along this line can be kept up, and indeed, some results in this manuscript have already made up a foundation for further exploration concerning the further progression of PU-algebras. These definitions and main results can be similarly extended to some other algebraic systems such as BCH-algebras, Hilbert algebras, BF-algebras, J-algebras, WS-algebras, CI-algebras, SU-algebras, BCL-algebras, BP-algebras and BO-algebras, Z- algebras and so forth. The main purpose of our future work is to investigate the fuzzy derivations ideals in PU-algebras, which may have a lot of applications in different branches of theoretical physics and computer science.
Published in | American Journal of Mathematical and Computer Modelling (Volume 6, Issue 1) |
DOI | 10.11648/j.ajmcm.20210601.13 |
Page(s) | 14-18 |
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), 2021. Published by Science Publishing Group |
PU-Algebras, (Left, Right)-derivations of PU-algebras, (Right, Left)-derivations of PU-algebras, Regular Derivations of PU-algebras.
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APA Style
Mehmood Khan, Dawood Khan, Khalida Mir Aalm. (2021). Characterization of Associative PU-algebras by the Notion of Derivations. American Journal of Mathematical and Computer Modelling, 6(1), 14-18. https://doi.org/10.11648/j.ajmcm.20210601.13
ACS Style
Mehmood Khan; Dawood Khan; Khalida Mir Aalm. Characterization of Associative PU-algebras by the Notion of Derivations. Am. J. Math. Comput. Model. 2021, 6(1), 14-18. doi: 10.11648/j.ajmcm.20210601.13
AMA Style
Mehmood Khan, Dawood Khan, Khalida Mir Aalm. Characterization of Associative PU-algebras by the Notion of Derivations. Am J Math Comput Model. 2021;6(1):14-18. doi: 10.11648/j.ajmcm.20210601.13
@article{10.11648/j.ajmcm.20210601.13, author = {Mehmood Khan and Dawood Khan and Khalida Mir Aalm}, title = {Characterization of Associative PU-algebras by the Notion of Derivations}, journal = {American Journal of Mathematical and Computer Modelling}, volume = {6}, number = {1}, pages = {14-18}, doi = {10.11648/j.ajmcm.20210601.13}, url = {https://doi.org/10.11648/j.ajmcm.20210601.13}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20210601.13}, abstract = {In this manuscript we insert the concept of derivations in associative PU-algebras and discuss some of its important results such that we prove that for a mapping being a (Left, Right) or (Right, Left)-derivation of an associative PU-algebra then such a mapping is one-one. If a mapping is regular then it is identity. If any element of an associative PU-algebra satisfying the criteria of identity function then such a map is identity. We also prove some useful properties for a mapping being (Left, Right)-regular derivation of an associative PU-algebra and (Right, Left)-regular derivation of an associative PU-algebra. Moreover we prove that if a mapping is regular (Left, Right)-derivation of an associative PU-algebra then its Kernel is a subalgebra. We have no doubt that the research along this line can be kept up, and indeed, some results in this manuscript have already made up a foundation for further exploration concerning the further progression of PU-algebras. These definitions and main results can be similarly extended to some other algebraic systems such as BCH-algebras, Hilbert algebras, BF-algebras, J-algebras, WS-algebras, CI-algebras, SU-algebras, BCL-algebras, BP-algebras and BO-algebras, Z- algebras and so forth. The main purpose of our future work is to investigate the fuzzy derivations ideals in PU-algebras, which may have a lot of applications in different branches of theoretical physics and computer science.}, year = {2021} }
TY - JOUR T1 - Characterization of Associative PU-algebras by the Notion of Derivations AU - Mehmood Khan AU - Dawood Khan AU - Khalida Mir Aalm Y1 - 2021/03/04 PY - 2021 N1 - https://doi.org/10.11648/j.ajmcm.20210601.13 DO - 10.11648/j.ajmcm.20210601.13 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 14 EP - 18 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20210601.13 AB - In this manuscript we insert the concept of derivations in associative PU-algebras and discuss some of its important results such that we prove that for a mapping being a (Left, Right) or (Right, Left)-derivation of an associative PU-algebra then such a mapping is one-one. If a mapping is regular then it is identity. If any element of an associative PU-algebra satisfying the criteria of identity function then such a map is identity. We also prove some useful properties for a mapping being (Left, Right)-regular derivation of an associative PU-algebra and (Right, Left)-regular derivation of an associative PU-algebra. Moreover we prove that if a mapping is regular (Left, Right)-derivation of an associative PU-algebra then its Kernel is a subalgebra. We have no doubt that the research along this line can be kept up, and indeed, some results in this manuscript have already made up a foundation for further exploration concerning the further progression of PU-algebras. These definitions and main results can be similarly extended to some other algebraic systems such as BCH-algebras, Hilbert algebras, BF-algebras, J-algebras, WS-algebras, CI-algebras, SU-algebras, BCL-algebras, BP-algebras and BO-algebras, Z- algebras and so forth. The main purpose of our future work is to investigate the fuzzy derivations ideals in PU-algebras, which may have a lot of applications in different branches of theoretical physics and computer science. VL - 6 IS - 1 ER -