TY  - JOUR
T1  - On the symmetric polynomials in the variety of Grassmann algebras
TT  - Grassmann cebirleri sınıfında simetrik polinomlar üzerine
AU  - Akdoğan, Nazan
PY  - 2021
DA  - December
DO  - 10.18185/erzifbed.732117
JF  - Erzincan University Journal of Science and Technology
PB  - Erzincan Binali Yildirim University
WT  - DergiPark
SN  - 2149-4584
SP  - 907
EP  - 913
VL  - 14
IS  - 3
LA  - en
AB  - 𝐾 karakteristiği sıfır olan bir cisim ve 𝐿, Grassmann cebirleri tarafından üretilen varyetede, 𝐾 cismi üzerinde rankı 2 olan birleşmeli cebir olsun. Bu çalışmada, 𝐿 cebirinin 𝐿𝑆2 simetrik polinomlar alt cebiri incelenmiş ve 𝐿𝑆2 için sonlu bir üreteç kümesi verilmiştir.
KW  - PI-algebra
KW  - Grassmann algebras
KW  - symmetric polynomial
N2  - Let K be a field of characteristic zero, and L be the associative algebra of rank 2 over K, in the variety generated by Grassmann algebras. In this paper we study the subalgebra L^(S_2 ) of symmetric polynomials in the algebra L, and give a finite generating set for L^(S_2 ).
CR  - Cox, D., Little, J. and O’Shea, D. (2015). “Ideals Varieties, and Algorithms 4th ed.”, Springer, New York, 345-352.
CR  - Drensky, V. (1996). “Free Algebras and PI-Algebras”, Springer, Singapore, 12-51.
CR  - Krakovski, D. and Regev, A. 1973. “The Polynomial Identities of the Grassmann Algebra”, Trans. Amer. Math. Soc., 181, 429-438.
CR  - Latyshev, V.N., 1976. “Partially Ordered Sets and Nonmatrix Identities of Associative Algebras” Algebr. Log., 15(1), 34-45.
CR  - Strumfels, B. (2008). “Algorithms in Invariant Theory 2nd ed.”, Springer-Verlag, Wien, 2-6.
CR  - van der Waerden, B.L. (1949). “Modern Algebra”, F. Ungar, New York, 78-82.
UR  - https://doi.org/10.18185/erzifbed.732117
L1  - https://dergipark.org.tr/en/download/article-file/1087205
ER  -