scholarly journals Divisor class groups of affine semigroup rings associated with distributive lattices

1992 ◽  
Vol 149 (2) ◽  
pp. 352-357 ◽  
Author(s):  
Mitsuyasu Hashimoto ◽  
Takayuki Hibi ◽  
Atsushi Noma
Keyword(s):  
Distributive Lattices ◽  
Semigroup Rings ◽  
Class Groups ◽  
Divisor Class ◽  
Affine Semigroup

scholarly journals Completions of rings of invariants and their divisor class groups

1978 ◽  
Vol 72 ◽  
pp. 71-82 ◽  
Author(s):  
Phillip Griffith
Keyword(s):  
Power Series ◽  
Maximal Ideal ◽  
Total Degree ◽  
Class Groups ◽  
Divisor Class ◽  
Power Series Ring ◽  
Series Ring ◽  
Formal Power Series Ring ◽  
Ring Of Polynomials ◽  
Formal Power

Let k be a field and let A = be a normal graded subring of the full ring of polynomials R = k[X1, · · ·, Xn] (where R always is graded via total degree and A0 = k). R. Fossum and the author [F-G] observed that the completion  at the irrelevant maximal ideal of A is isomorphic to the subring of the formal power series ring R̂ = k[[X1, · ·., Xn]] and, moreover, that  is a ring of invariants of an algebraic group whenever A is.

scholarly journals Torsion in kernels of induced maps on divisor class groups

2015 ◽  
Vol 14 (08) ◽  
pp. 1550123
Author(s):  
Sean Sather-Wagstaff ◽  
Sandra Spiroff
Keyword(s):  
Projective Dimension ◽  
Class Groups ◽  
Divisor Class ◽  
Finite Projective Dimension ◽  
Induced Maps

We investigate torsion elements in the kernel of the map on divisor class groups of excellent local normal domains A and A/I, for an ideal I of finite projective dimension. The motivation for this work is a result of Griffith–Weston which applies when I is principal.

scholarly journals Divisor Class Groups on Algebraic Varieties

1953 ◽  
Vol 39 (8) ◽  
pp. 872-877 ◽  
Author(s):  
K. Kodaira ◽  
D. C. Spencer
Keyword(s):  
Algebraic Varieties ◽  
Class Groups ◽  
Divisor Class
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