RM ALGEBRAS AND COMMUTATIVE MOONS

Yıl 2021, Cilt: 29 Sayı: 29, 95 - 106, 05.01.2021

Andrzej Walendzıak

https://doi.org/10.24330/ieja.852024

Cited By: 1

Öz

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.

Anahtar Kelimeler

RM, BH, CI, BCH, BCI algebra, moon, p-semisimplicity

Kaynakça

• 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.