A Presentation of The Frege Lie Algebra F/γ3 (F)'

Gülistan Kaya Gök

doi:10.36753/mathenot.421354

Research Article

Year 2016, Volume: 4 Issue: 1, 24 - 30, 15.04.2016

Gülistan Kaya Gök

https://doi.org/10.36753/mathenot.421354

Abstract

References

[1] Bergman, G. M., The Diamond lemma for ring theory, Adv. in Math. 29 (1978), 178-218.
[2] Bokut, L. A., Unsolvability of the word problem and subalgebras of finitely presented Lie algebras, Izv. Akad. Nauk. SSSR Ser. Math. 36 (1972), 1173-1219.
[3] Bokut, L. A., Embeddings into simple associative algebras, Algebrai Logika 15 (1976), 117-142.
[4] Bokut, L. A., Algorithmic and Combinatorial Algebra, Kluwer, Dordrecht, (1994).
[5] Bokut, L. A., Kolesnikov, P., Gröbner-Shirshov bases: from incipient to nowadays, Proceedings of the POMI 272 (1994), 26-67.
[6] Bokut, L. A., Kolesnikov, P., Gröbner-Shirshov bases: from their incipiency to the present, J. Math. Sci. 116, 1 (2003), 2894-2916.
[7] Bokut, L. A., Chen, Y., Gröbner-Shirshov bases: some new results, Proc. Second Int. Congress in Algebra and Combinatorics,World Scientific, (2008), 35-56.
[8] Buchberger, B., An algorithm for finding a basis for the residue class Ring of a zero-dimensional polynomial ideal, Phd. thesis, Univ. of Innsbruck, Austria, (1965).
[9] Buchberger, B., An algorithmical criteria for the solvability of algebraic system of equations, Aequationes Math., 4 (1970), 374- 383.
[10] Drensky, V., Defining relations of noncommutative algebras, Institue of Mathematics and Informatics Bulgarian Academy of Sciences.
[11] Shirshov, A.I., Some algorithmic problems for Lie algebras, Sibirsk. Mat. Z. 3 (1962) 292-296; English translation in SIGSAM Bull, 33(2) (1999), 3-6.
[12] Smel’kin, A. L., Free polynilpotent groups I. Soviet Math. Dokl. 4 (1963), 950-953. II. Izvest. Akad. Nauk S.S.S.R. Ser. Mat. 28(1964), 91-122. III. Dokl. Akad. Nauk. S.S.S.R. 169 (1966), 1024-1025.

A Presentation of The Frege Lie Algebra F/γ3 (F)'

Year 2016, Volume: 4 Issue: 1, 24 - 30, 15.04.2016

Gülistan Kaya Gök

https://doi.org/10.36753/mathenot.421354

Abstract

Keywords

Free Lie algebra, Presentation, Gröbner basis

References

[1] Bergman, G. M., The Diamond lemma for ring theory, Adv. in Math. 29 (1978), 178-218.
[2] Bokut, L. A., Unsolvability of the word problem and subalgebras of finitely presented Lie algebras, Izv. Akad. Nauk. SSSR Ser. Math. 36 (1972), 1173-1219.
[3] Bokut, L. A., Embeddings into simple associative algebras, Algebrai Logika 15 (1976), 117-142.
[4] Bokut, L. A., Algorithmic and Combinatorial Algebra, Kluwer, Dordrecht, (1994).
[5] Bokut, L. A., Kolesnikov, P., Gröbner-Shirshov bases: from incipient to nowadays, Proceedings of the POMI 272 (1994), 26-67.
[6] Bokut, L. A., Kolesnikov, P., Gröbner-Shirshov bases: from their incipiency to the present, J. Math. Sci. 116, 1 (2003), 2894-2916.
[7] Bokut, L. A., Chen, Y., Gröbner-Shirshov bases: some new results, Proc. Second Int. Congress in Algebra and Combinatorics,World Scientific, (2008), 35-56.
[8] Buchberger, B., An algorithm for finding a basis for the residue class Ring of a zero-dimensional polynomial ideal, Phd. thesis, Univ. of Innsbruck, Austria, (1965).
[9] Buchberger, B., An algorithmical criteria for the solvability of algebraic system of equations, Aequationes Math., 4 (1970), 374- 383.
[10] Drensky, V., Defining relations of noncommutative algebras, Institue of Mathematics and Informatics Bulgarian Academy of Sciences.
[11] Shirshov, A.I., Some algorithmic problems for Lie algebras, Sibirsk. Mat. Z. 3 (1962) 292-296; English translation in SIGSAM Bull, 33(2) (1999), 3-6.
[12] Smel’kin, A. L., Free polynilpotent groups I. Soviet Math. Dokl. 4 (1963), 950-953. II. Izvest. Akad. Nauk S.S.S.R. Ser. Mat. 28(1964), 91-122. III. Dokl. Akad. Nauk. S.S.S.R. 169 (1966), 1024-1025.

There are 12 citations in total.

Details

Primary Language	English
Journal Section	Articles
Authors	Gülistan Kaya Gök
Publication Date	April 15, 2016
Submission Date	August 18, 2015
Published in Issue	Year 2016 Volume: 4 Issue: 1

Cite

APA	Gök, G. K. (2016). A Presentation of The Frege Lie Algebra F/γ3 (F)’. Mathematical Sciences and Applications E-Notes, 4(1), 24-30. https://doi.org/10.36753/mathenot.421354
AMA	Gök GK. A Presentation of The Frege Lie Algebra F/γ3 (F)’. Math. Sci. Appl. E-Notes. April 2016;4(1):24-30. doi:10.36753/mathenot.421354
Chicago	Gök, Gülistan Kaya. “A Presentation of The Frege Lie Algebra F/γ3 (F)’”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 24-30. https://doi.org/10.36753/mathenot.421354.
EndNote	Gök GK (April 1, 2016) A Presentation of The Frege Lie Algebra F/γ3 (F)’. Mathematical Sciences and Applications E-Notes 4 1 24–30.
IEEE	G. K. Gök, “A Presentation of The Frege Lie Algebra F/γ3 (F)’”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 24–30, 2016, doi: 10.36753/mathenot.421354.
ISNAD	Gök, Gülistan Kaya. “A Presentation of The Frege Lie Algebra F/γ3 (F)’”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 24-30. https://doi.org/10.36753/mathenot.421354.
JAMA	Gök GK. A Presentation of The Frege Lie Algebra F/γ3 (F)’. Math. Sci. Appl. E-Notes. 2016;4:24–30.
MLA	Gök, Gülistan Kaya. “A Presentation of The Frege Lie Algebra F/γ3 (F)’”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 24-30, doi:10.36753/mathenot.421354.
Vancouver	Gök GK. A Presentation of The Frege Lie Algebra F/γ3 (F)’. Math. Sci. Appl. E-Notes. 2016;4(1):24-30.