Research Article
BibTex RIS Cite

Direct Product of Bitonic Algebras

Year 2022, Volume: 12 Issue: 1, 56 - 69, 30.06.2022
https://doi.org/10.37094/adyujsci.1049322

Abstract

The purpose of this study is to construct the concept of direct product of bitonic algebras, and investigate some respective features. Also, the concept of direct product of commutative bitonic algebras, bitonic homomorphism are studied. Then the notion of direct product of bitonic algebras is expanded to finite family of bitonic algebras and their qualifications are practised.

References

  • [1] Komori, Y., The class of BCC-algebras is not variety, Mathematica Japonica, 29 (3), 391-394, 1984.
  • [2] Dudek, W.A., The number of subalgebras of finite BCC-algebras, Bulletin of the Institute of Mathematics, 20 (2), 129-135, 1992.
  • [3] Iseki, K., An algebra related with a propositional calculus, Proceedings of the Japan Academy, 42 (1), 26-29, 1966.
  • [4] Iseki, K., Tanaka, S., An Introduction to the theory of BCK-algebras, Mathematica Japonica, 23, 1-26, 1978.
  • [5] Borzooei, R.A., Khosravi Shoar, S., Implication algebras are equivalent to the dual implicative BCK-algebras, Scientiae Mathematicae Japonicae, 63 (3), 429-431, 2006.
  • [6] Kim, K.H., Yon, Y.H., Dual BCK-algebra and MV-algebra, Scientiae Mathematicae Japonicae, 66 (2), 247-253, 2007.
  • [7] Yon, Y.H., Kim, K.H., On Heyting algebras and dual BCK-algebras, Bulletin of the Iranian Mathematical Society, 38 (1), 159-168, 2012.
  • [8] Diego, A., Sur lès algèbres de Hilbert, Collection de Logique Mathématique, Sèr. A., 21, 1966.
  • [9] Halas, R., Remarks on commutative Hilbert algebras, Mathematica Bohemica, 127 (4), 525-529, 2002.
  • [10] Henkin, L., An algebraic characterization of quantifiers, Fundamenta Mathematicae, 37, 63-74, 1950.
  • [11] Marsden, E.L., Compatible elements in implicative models, Journal of Philosophical Logic, 1, 156-161, 1972.
  • [12] Curry, H.B., Foundations of Mathematical Logic, McGraw-Hill, New York, 1963.
  • [13] Birkhoff, G., Lattice Theory, American Mathematical Society Colloquium Publications, Providence, RI., 1967.
  • [14] Abbot, J.C., Algebras of implication and semi-lattices, Sèminarire Dubreil (Algèbre et thèorie des nombres), 20e (2), exp., no 20, 1-8, 1966-1967.
  • [15] Xu, Y., Lattice implication algebras, Journal of Southwest Jiaotong University., 1, 20- 27, 1993.
  • [16] Xu, Y., Lattice H implication algebras and lattice implication algebra classes, Journal of Hebei Mining and Civil Engineering Institute, 3, 139-143, 1992.
  • [17] Yon, Y.H., Ayar Özbal, Ş., On derivations and generalized derivations of bitonic algebras, Applicable Analysis and Discrete Mathematics, 12, 110-125, 2018.
  • [18] Lingcong, J.A.V, Endam, J.C., Direct product of B-algebras, International Journal of Algebra, 10, 33-40, (2016).
  • [19] Setani, A., Gemawati, S., Deswita, L., Direct product of BP-algebras, International Journal of Mathematics Trends and Technology, 66 (10), 63-69, 2020.

Bitonic Cebirlerin Direkt Çarpımları

Year 2022, Volume: 12 Issue: 1, 56 - 69, 30.06.2022
https://doi.org/10.37094/adyujsci.1049322

Abstract

Bu çalışmanın amacı bitonic cebirlerin direkt çarpımları olup bitonic cebirlerin direkt çarpımlarının ilgili özelliklerini çalışmaktır. Ayrıca, değişmeli bitonic cebirlerinin direkt çarpımları, bitonic homomorfizmalar incelenmiş ve değişmeli bitonic cebirlerin direkt çarpımlarının da değişmeli olduğu elde edilmiş ve direkt çarpımların homomorfizmaları da çalışılmıştır.

References

  • [1] Komori, Y., The class of BCC-algebras is not variety, Mathematica Japonica, 29 (3), 391-394, 1984.
  • [2] Dudek, W.A., The number of subalgebras of finite BCC-algebras, Bulletin of the Institute of Mathematics, 20 (2), 129-135, 1992.
  • [3] Iseki, K., An algebra related with a propositional calculus, Proceedings of the Japan Academy, 42 (1), 26-29, 1966.
  • [4] Iseki, K., Tanaka, S., An Introduction to the theory of BCK-algebras, Mathematica Japonica, 23, 1-26, 1978.
  • [5] Borzooei, R.A., Khosravi Shoar, S., Implication algebras are equivalent to the dual implicative BCK-algebras, Scientiae Mathematicae Japonicae, 63 (3), 429-431, 2006.
  • [6] Kim, K.H., Yon, Y.H., Dual BCK-algebra and MV-algebra, Scientiae Mathematicae Japonicae, 66 (2), 247-253, 2007.
  • [7] Yon, Y.H., Kim, K.H., On Heyting algebras and dual BCK-algebras, Bulletin of the Iranian Mathematical Society, 38 (1), 159-168, 2012.
  • [8] Diego, A., Sur lès algèbres de Hilbert, Collection de Logique Mathématique, Sèr. A., 21, 1966.
  • [9] Halas, R., Remarks on commutative Hilbert algebras, Mathematica Bohemica, 127 (4), 525-529, 2002.
  • [10] Henkin, L., An algebraic characterization of quantifiers, Fundamenta Mathematicae, 37, 63-74, 1950.
  • [11] Marsden, E.L., Compatible elements in implicative models, Journal of Philosophical Logic, 1, 156-161, 1972.
  • [12] Curry, H.B., Foundations of Mathematical Logic, McGraw-Hill, New York, 1963.
  • [13] Birkhoff, G., Lattice Theory, American Mathematical Society Colloquium Publications, Providence, RI., 1967.
  • [14] Abbot, J.C., Algebras of implication and semi-lattices, Sèminarire Dubreil (Algèbre et thèorie des nombres), 20e (2), exp., no 20, 1-8, 1966-1967.
  • [15] Xu, Y., Lattice implication algebras, Journal of Southwest Jiaotong University., 1, 20- 27, 1993.
  • [16] Xu, Y., Lattice H implication algebras and lattice implication algebra classes, Journal of Hebei Mining and Civil Engineering Institute, 3, 139-143, 1992.
  • [17] Yon, Y.H., Ayar Özbal, Ş., On derivations and generalized derivations of bitonic algebras, Applicable Analysis and Discrete Mathematics, 12, 110-125, 2018.
  • [18] Lingcong, J.A.V, Endam, J.C., Direct product of B-algebras, International Journal of Algebra, 10, 33-40, (2016).
  • [19] Setani, A., Gemawati, S., Deswita, L., Direct product of BP-algebras, International Journal of Mathematics Trends and Technology, 66 (10), 63-69, 2020.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Şule Ayar Özbal 0000-0001-5933-5858

Publication Date June 30, 2022
Submission Date January 3, 2022
Acceptance Date April 21, 2022
Published in Issue Year 2022 Volume: 12 Issue: 1

Cite

APA Ayar Özbal, Ş. (2022). Direct Product of Bitonic Algebras. Adıyaman University Journal of Science, 12(1), 56-69. https://doi.org/10.37094/adyujsci.1049322
AMA Ayar Özbal Ş. Direct Product of Bitonic Algebras. ADYU J SCI. June 2022;12(1):56-69. doi:10.37094/adyujsci.1049322
Chicago Ayar Özbal, Şule. “Direct Product of Bitonic Algebras”. Adıyaman University Journal of Science 12, no. 1 (June 2022): 56-69. https://doi.org/10.37094/adyujsci.1049322.
EndNote Ayar Özbal Ş (June 1, 2022) Direct Product of Bitonic Algebras. Adıyaman University Journal of Science 12 1 56–69.
IEEE Ş. Ayar Özbal, “Direct Product of Bitonic Algebras”, ADYU J SCI, vol. 12, no. 1, pp. 56–69, 2022, doi: 10.37094/adyujsci.1049322.
ISNAD Ayar Özbal, Şule. “Direct Product of Bitonic Algebras”. Adıyaman University Journal of Science 12/1 (June 2022), 56-69. https://doi.org/10.37094/adyujsci.1049322.
JAMA Ayar Özbal Ş. Direct Product of Bitonic Algebras. ADYU J SCI. 2022;12:56–69.
MLA Ayar Özbal, Şule. “Direct Product of Bitonic Algebras”. Adıyaman University Journal of Science, vol. 12, no. 1, 2022, pp. 56-69, doi:10.37094/adyujsci.1049322.
Vancouver Ayar Özbal Ş. Direct Product of Bitonic Algebras. ADYU J SCI. 2022;12(1):56-69.

...