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RM ALGEBRAS AND COMMUTATIVE MOONS

Year 2021, , 95 - 106, 05.01.2021
https://doi.org/10.24330/ieja.852024

Abstract

Some generalizations of BCI algebras (the RM, BH, CI, BCH,
BH**, BCH**, and *aRM** algebras) satisfying the identity $(x \rightarrow
1)\rightarrow y = (y \rightarrow 1) \rightarrow x$ are considered. The connections of these algebras
and various generalizations of commutative groups (such as, for
example, involutive commutative moons and commutative (weakly)
goops) are described. In particular, it is proved that an RM
algebra verifying this identity is equivalent to an involutive
commutative moon.

References

  • M. Aslam and A. B. Thaheem, A note on p-semisimple BCI-algebras, Math. Japon., 36 (1991), 39-45.
  • Q. P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ., 11 (1983), 313-320.
  • A. Iorgulescu, New generalizations of BCI, BCK and Hilbert algebras - Part I, J. Mult.-Valued Logic Soft Comput., 27(4) (2016), 353-406.
  • A. Iorgulescu, New generalizations of BCI, BCK and Hilbert algebras - Part II, J. Mult.-Valued Logic Soft Comput., 27(4) (2016), 407-456.
  • A. Iorgulescu, Implicative-Groups vs. Groups and Generalizations, Matrix Rom, Bucharest, 2018.
  • K. Iseki, An algebra related with a propositional calculus, Proc. Japan. Acad., 42 (1966), 26-29.
  • Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Sci. Math., 1(3) (1998), 347-354.
  • H. S. Kim and H. G. Park, On 0-commutative B-algebras, Sci. Math. Jpn., 62(1) (2005), 7-12, e-2005: 31-36.
  • T. Lei and C. Xi, p-radical in BCI-algebras, Math. Japon., 30 (1985), 511-517.
  • D. J. Meng, BCI-algebras and abelian groups, Math. Japon., 32 (1987), 693-696.
  • B. L. Meng, CI-algebras, Sci. Math. Jpn., 71 (2010), 11-17; e-2009: 695-701.
  • A. Walendziak, Deductive systems and congruences in RM algebras, J. Mult.-Valued Logic Soft Comput., 30 (2018), 521-539.
  • A. Walendziak, The implicative property for some generalizations of BCK algebras, J. Mult.-Valued Logic Soft Comput., 31 (2018), 591-611.
  • A.Walendziak, The property of commutativity for some generalizations of BCK algebras, Soft Comput., 23 (2019), 7505-7511.
  • A.Walendziak, Some generalizations of p-semisimple BCI algebras and groups, Soft Comput., 24 (2020), 12781-12787.
  • Q. Zhang, Some other characterizations of p-semisimple BCI-algebras, Math. Japon., 36 (1991), 815-817.
Year 2021, , 95 - 106, 05.01.2021
https://doi.org/10.24330/ieja.852024

Abstract

References

  • M. Aslam and A. B. Thaheem, A note on p-semisimple BCI-algebras, Math. Japon., 36 (1991), 39-45.
  • Q. P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ., 11 (1983), 313-320.
  • A. Iorgulescu, New generalizations of BCI, BCK and Hilbert algebras - Part I, J. Mult.-Valued Logic Soft Comput., 27(4) (2016), 353-406.
  • A. Iorgulescu, New generalizations of BCI, BCK and Hilbert algebras - Part II, J. Mult.-Valued Logic Soft Comput., 27(4) (2016), 407-456.
  • A. Iorgulescu, Implicative-Groups vs. Groups and Generalizations, Matrix Rom, Bucharest, 2018.
  • K. Iseki, An algebra related with a propositional calculus, Proc. Japan. Acad., 42 (1966), 26-29.
  • Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Sci. Math., 1(3) (1998), 347-354.
  • H. S. Kim and H. G. Park, On 0-commutative B-algebras, Sci. Math. Jpn., 62(1) (2005), 7-12, e-2005: 31-36.
  • T. Lei and C. Xi, p-radical in BCI-algebras, Math. Japon., 30 (1985), 511-517.
  • D. J. Meng, BCI-algebras and abelian groups, Math. Japon., 32 (1987), 693-696.
  • B. L. Meng, CI-algebras, Sci. Math. Jpn., 71 (2010), 11-17; e-2009: 695-701.
  • A. Walendziak, Deductive systems and congruences in RM algebras, J. Mult.-Valued Logic Soft Comput., 30 (2018), 521-539.
  • A. Walendziak, The implicative property for some generalizations of BCK algebras, J. Mult.-Valued Logic Soft Comput., 31 (2018), 591-611.
  • A.Walendziak, The property of commutativity for some generalizations of BCK algebras, Soft Comput., 23 (2019), 7505-7511.
  • A.Walendziak, Some generalizations of p-semisimple BCI algebras and groups, Soft Comput., 24 (2020), 12781-12787.
  • Q. Zhang, Some other characterizations of p-semisimple BCI-algebras, Math. Japon., 36 (1991), 815-817.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Andrzej Walendzıak This is me

Publication Date January 5, 2021
Published in Issue Year 2021

Cite

APA Walendzıak, A. (2021). RM ALGEBRAS AND COMMUTATIVE MOONS. International Electronic Journal of Algebra, 29(29), 95-106. https://doi.org/10.24330/ieja.852024
AMA Walendzıak A. RM ALGEBRAS AND COMMUTATIVE MOONS. IEJA. January 2021;29(29):95-106. doi:10.24330/ieja.852024
Chicago Walendzıak, Andrzej. “RM ALGEBRAS AND COMMUTATIVE MOONS”. International Electronic Journal of Algebra 29, no. 29 (January 2021): 95-106. https://doi.org/10.24330/ieja.852024.
EndNote Walendzıak A (January 1, 2021) RM ALGEBRAS AND COMMUTATIVE MOONS. International Electronic Journal of Algebra 29 29 95–106.
IEEE A. Walendzıak, “RM ALGEBRAS AND COMMUTATIVE MOONS”, IEJA, vol. 29, no. 29, pp. 95–106, 2021, doi: 10.24330/ieja.852024.
ISNAD Walendzıak, Andrzej. “RM ALGEBRAS AND COMMUTATIVE MOONS”. International Electronic Journal of Algebra 29/29 (January 2021), 95-106. https://doi.org/10.24330/ieja.852024.
JAMA Walendzıak A. RM ALGEBRAS AND COMMUTATIVE MOONS. IEJA. 2021;29:95–106.
MLA Walendzıak, Andrzej. “RM ALGEBRAS AND COMMUTATIVE MOONS”. International Electronic Journal of Algebra, vol. 29, no. 29, 2021, pp. 95-106, doi:10.24330/ieja.852024.
Vancouver Walendzıak A. RM ALGEBRAS AND COMMUTATIVE MOONS. IEJA. 2021;29(29):95-106.