### fq-derivasi di BM-aljabar

Egytia Yattaqi, Sri Gemawati, Ihda Hasbiyati

#### Abstract

ABSTRAK

B-aljabar adalah suatu himpunan tak kosong X dengan operasi biner  dan konstanta 0 yang memenuhi aksioma-aksioma tertentu. Suatu bentuk khusus dari B-aljabar adalah BM-aljabar. Adapun hubungan kedua aljabar tersebut, setiap BM-aljabar adalah B-aljabar dan setiap B-aljabar 0-komutatif adalah BM-aljabar. Konsep fq-derivasi telah dibahas di B-aljabar. Pada artikel ini, dibahas konsep fq-derivasi di BM-aljabar. Hasil penelitian yang diperoleh adalah mendefinisikan inside dan outside fq-derivasi di BM-aljabar dan menentukan sifat-sifatnya. Adapun definisi fq-derivasi di BM-aljabar ekuivalen dengan fq-derivasi di B-aljabar, namun pada sifat-sifatnya terdapat perbedaan, yaitu terdapat sifat fq-derivasi yang berlaku di BM-aljabar tetapi secara umum tidak berlaku di B-aljabar.

ABSTRACT

B-algebra is a non-empty set X with a constant 0 and binary operation satisfying certain axioms. A special form of B-algebra is BM-algebra. Their relationship are every BM-algebra is a B-algebra and every 0-commutative B-algebra is a BM-algebra.  The concept of fq-derivation in B-algebra is discussed. The results define inside and outside fq-derivations in BM-algebra and obtain related properties. Moreover, the definition of fq-derivation in BM-algebra is equivalent to fq-derivation in B-algebra, but there are differences in their properties, which is there are some properties of fq-derivation in BM-algebra, but generally don’t hold in B-algebra.

#### Keywords

BM-algebra; Inside fq-derivation; Outside fq-derivation; fq-derivation

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#### References

J. Neggers and H. S Kim, “On B-algebras,” Mat. Vesn., vol. 54, no. 1–2, pp. 21–29, 2002.

H. S. Kim and H. G. Park, “On 0-commutative B-algebras,” Sci. Math. Jpn., vol. 62, no. 1, pp. 31–36, 2005.

C. B. Kim and H. S. Kim, “On BM-algebras,” Sci. Math. Jpn., vol. 63, no. 3, pp. 421–428, 2006.

M. Ashraf, S. Ali, and C. Haetinger, “On derivations in rings and their applications,” Aligarh Bull Math, vol. 25, no. 2, pp. 79–107, 2006.

N. Alshehri, “Derivations of B-algebras,” Science (80-. )., vol. 22, no. 1, 2010.

K. Sugianti and S. Gemawati, “Generalized Derivations of BM-Algebras,” Int. J. Contemp. Math. Sci., vol. 15, no. 4, pp. 225–233, 2020.

D. Al-Kadi, “fq-Derivations of G-Algebra,” 2016.

P. Muangkarn, C. Suanoom, P. Pengyim, and A. Iampan, “fq-Derivations of B-algebras,” J. Math. Comput. Sci., vol. 11, no. 2, pp. 2047–2057, 2021.

C. Ramadhona, S. Gemawati, and Syamsudhuha, “Generalized f-derivation of BP-algebras,” Int. J. Math. Trends Technol., vol. 66, no. 11, pp. 80–86, 2020.

N. Kandaraj and A. Devi A, “f-derivations on BP-algebras,” Int. J. Sci. Res. Publ., vol. 6, no. 10, pp. 8–18, 2016.

W. Aziz, S. Gemawati, and L. Deswita, “On (f, g)-derivations in BG-algebras,” Int. Organ. Sci. Res. J. Math., vol. 16, pp. 14–20, 2020.

Kamaludin, S. Gemawati, and Kartini, “Derivations in BG-algebras,” Int. J. Algebr., vol. 13, no. 5, pp. 249–257, 2019.

T. Ganeshkumar and M. Chandramouleeswaran, “t-derivations on TM-algebras,” Int. J. Pure Appl. Math., vol. 85, no. 1, pp. 95–107, 2013.

R. Soleimani and S. Jahangiri, “A Note on t-derivations of B-algebras.”

H. S. Kim, Y. H. Kim, and J. Neggers, “Coxeters and pre-Coxeter algebras in Smarandache setting,” Honam Math. J., vol. 26, no. 4, pp. 471–481, 2004.

DOI: https://doi.org/10.34312/jjom.v3i2.10379

Copyright (c) 2021 Egytia Yattaqi, Sri Gemawati, Ihda Hasbiyati 