Quantum Algebra From Generalized Q-Algebra
Keywords:
Q-algebras; BCI/BCK/BCH-algebra; quantum mechanics
Abstract
The paper contains an investigation of the notion of Q-algebras. A brief introduction to
quantum mechanics is given.
A brief introduction to BCI/BCK/BCH-algebra are given. A new generalization of Q-algebra
has been introduced. The Q- quantum algebra has been studied.
Various examples have been given.
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References
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(2000) 493-498.
[12] Y.B. Jun and X.L. Xin, Positive implicative hyper BCK-algebras, Sci. Math. Jpn., 55 (2002) 97-106.
[13] G. Georgescu, A. Iorgulescu, Pseudo-BCK algebras: An extension of BCK-algebras, Proceedings of
DMTCS'01: Combinatorics, Computability and Logic, Springer, London, (2001) 97-114.
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[15] P. Hajek, Observations on non-commutative fuzzy logic, Soft Computing, 8 (2003) 38-43.
[16] Y.S. Huang, BCI-algebras, Science Press, China, 2006.
[17] C.S. Hoo, MV-algebras, ideals and semisimplicity, Math. Japon, 34 (1989) 563-583.
[18] H.S. Kim and Y.H. Kim, On BE-algebras, Sci, Math, Jpn., 66, 1 (2007) 113-119.
[19] F. Marty, Sur une generalization de la notion de groupe, 8iem Congres math Scandinaves, Stockholm,
(1934) 45-49 (french).
[20] J. Meng and Y.B. Jun, BCK-algebras, Kyung Moon Sa Co, Korea, 1994.
[21] D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCK-algebras, Math.
Japon., 31 (1986) 889-894.
[22] A. Rezaei, A. Borumand Saeid and A. Rradfar, On eBE-algebras, TWMS J. Pure Appl. Math., 7, 2
(2016), 200-210.
[23] M.M. Zahedi, R.A. Borzooei, Y.B. Jun and A. Hasankhani, Some results on hyper K-algebras, Sci.
Math, Jpn., 3, 1 (2000) 53-59.
[24] X.H. Zhang, BIK+-logic and non-commutative fuzzy logics, Fuzzy Systems Math., 21 (2007) 31-36.
[25] P. Woit, Quantum Theory, Groups and Representations, Department of Mathematics, Columbia Uni-
versity, 2017.
749-757.
[2] A. Rradfar,A. Rezaei and A. Borumand Saeid , Extensions of BCK-algebras, PURE MATHEMATICS RESEARCH ARTICLE, (2010): 06D20; 06F35; 03G25.
[3] C.C. Chang, Algebraic analysis of many-valued logics, Trans. Amer. Math. Soc., 88 (1958) 467-490.
[4] L.C. Ciungu, Non-commutative Multiple-Valued Logic Algebras, Springer, 2014.
[5] R.A. Borzooei, A. Hasankhani, M. M. Zahedi and Y. B. Jun, On hyper K-algebras, Math. Jpn., 52, 1
(2000) 113-121.
[6] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV Proc. Japan Academy, 42 (1966)
19-22.
[7] A. Iorgulescu, Algebras of logic as BCK-algebras, Academy of Economic Studies Press, Bucharest, 2008.
[8] K. Iseki, An algebra related with propositional calculus, XIV Proc. Japan Academy, 42 (1966) 26-29.
[9] K. Iseki, On BCI-algebras, Math. Sem. Notes, Kobe Univ., 8 (1980) 125{130.
[10] Y.B. Jun, M.M. Zahedi, X.L. Xin and R.A. Borzooei, On hyper BCK-algebras, Ital. J. Pure Appl.
Math., 8 (2000) 127-136.
[11] Y.B. Jun, M. M. Zahedi, X.L. Xin and E.H. Rohi, Strong hyper BCK-algebras, Sci. Math. Jpn., 51,3
(2000) 493-498.
[12] Y.B. Jun and X.L. Xin, Positive implicative hyper BCK-algebras, Sci. Math. Jpn., 55 (2002) 97-106.
[13] G. Georgescu, A. Iorgulescu, Pseudo-BCK algebras: An extension of BCK-algebras, Proceedings of
DMTCS'01: Combinatorics, Computability and Logic, Springer, London, (2001) 97-114.
[14] P. Hajek, Mathemathematics of fuzzy logic, Kluwer Academic Publishers, Dordrecht, (1998).
[15] P. Hajek, Observations on non-commutative fuzzy logic, Soft Computing, 8 (2003) 38-43.
[16] Y.S. Huang, BCI-algebras, Science Press, China, 2006.
[17] C.S. Hoo, MV-algebras, ideals and semisimplicity, Math. Japon, 34 (1989) 563-583.
[18] H.S. Kim and Y.H. Kim, On BE-algebras, Sci, Math, Jpn., 66, 1 (2007) 113-119.
[19] F. Marty, Sur une generalization de la notion de groupe, 8iem Congres math Scandinaves, Stockholm,
(1934) 45-49 (french).
[20] J. Meng and Y.B. Jun, BCK-algebras, Kyung Moon Sa Co, Korea, 1994.
[21] D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCK-algebras, Math.
Japon., 31 (1986) 889-894.
[22] A. Rezaei, A. Borumand Saeid and A. Rradfar, On eBE-algebras, TWMS J. Pure Appl. Math., 7, 2
(2016), 200-210.
[23] M.M. Zahedi, R.A. Borzooei, Y.B. Jun and A. Hasankhani, Some results on hyper K-algebras, Sci.
Math, Jpn., 3, 1 (2000) 53-59.
[24] X.H. Zhang, BIK+-logic and non-commutative fuzzy logics, Fuzzy Systems Math., 21 (2007) 31-36.
[25] P. Woit, Quantum Theory, Groups and Representations, Department of Mathematics, Columbia Uni-
versity, 2017.
Published
2021-07-26
How to Cite
Tabuni, M. (2021). Quantum Algebra From Generalized Q-Algebra. Journal of Progressive Research in Mathematics, 18(3), 17-23. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/2066
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