scholarly journals Codes over affine algebras with a finite commutative chain coefficient ring

2018 ◽  
Vol 49 ◽  
pp. 94-107 ◽  
Author(s):  
E. Martínez-Moro ◽  
A. Piñera-Nicolás ◽  
I.F. Rúa
Keyword(s):  
Affine Algebras ◽  
Coefficient Ring

scholarly journals Connections, Poisson Brackets, and Affine Algebras

1996 ◽  
Vol 180 (3) ◽  
pp. 757-777 ◽  
Author(s):  
Daniel R. Farkas
Keyword(s):  
Poisson Brackets ◽  
Affine Algebras

Quantum affine algebras

1991 ◽  
Vol 142 (2) ◽  
pp. 261-283 ◽  
Author(s):  
Vyjayanthi Chari ◽  
Andrew Pressley
Keyword(s):  
Quantum Affine Algebras ◽  
Affine Algebras

Standard modules of quantum affine algebras

2002 ◽  
Vol 111 (3) ◽  
pp. 509-533 ◽  
Author(s):  
E. Vasserot ◽  
M. Varagnolo
Keyword(s):  
Quantum Affine Algebras ◽  
Affine Algebras

scholarly journals Symmetric quiver Hecke algebras andR-matrices of quantum affine algebras III: Table 1.

2015 ◽  
Vol 111 (2) ◽  
pp. 420-444 ◽  
Author(s):  
Seok-Jin Kang ◽  
Masaki Kashiwara ◽  
Myungho Kim ◽  
Se-jin Oh
Keyword(s):  
Hecke Algebras ◽  
Quantum Affine Algebras ◽  
Affine Algebras

scholarly journals Gröbner bases and products of coefficient rings

2002 ◽  
Vol 65 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Graham H. Norton ◽  
Ana Sӑlӑgean
Keyword(s):  
Gröbner Basis ◽  
Chinese Remainder Theorem ◽  
Gröbner Bases ◽  
Commutative Rings ◽  
Grobner Bases ◽  
Grobner Basis ◽  
Know How ◽  
Elementary Method ◽  
Coefficient Ring ◽  
Finite Direct Product

Suppose that A is a finite direct product of commutative rings. We show from first principles that a Gröbner basis for an ideal of A[x1,…,xn] can be easily obtained by ‘joining’ Gröbner bases of the projected ideals with coefficients in the factors of A (which can themselves be obtained in parallel). Similarly for strong Gröbner bases. This gives an elementary method of constructing a (strong) Gröbner basis when the Chinese Remainder Theorem applies to the coefficient ring and we know how to compute (strong) Gröbner bases in each factor.

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