scholarly journals ON THE DIVISOR-CLASS GROUP OF MONADIC SUBMONOIDS OF RINGS OF INTEGER-VALUED POLYNOMIALS

2017 ◽  
Vol 32 (2) ◽  
pp. 233-260
Author(s):  
Andreas Reinhart
Keyword(s):  
Class Group ◽  
Divisor Class Group ◽  
Divisor Class

scholarly journals Some factorization properties of Krull domains with infinite cyclic divisor class group

1994 ◽  
Vol 96 (2) ◽  
pp. 97-112 ◽  
Author(s):  
David F. Anderson ◽  
Scott T. Chapman ◽  
William W. Smith
Keyword(s):  
Class Group ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Krull Domains

scholarly journals The divisor class group of a Quot scheme

2010 ◽  
Vol 3 (0) ◽  
pp. 1-14
Author(s):  
Rafael Hernández ◽  
Daniel Ortega
Keyword(s):  
Class Group ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Quot Scheme

scholarly journals ON FACTORIZATION IN BLOCK MONOIDS FORMED BY $\{\bar{1},\bar{a}\}$ IN $\mathbb{Z}_{n}$

2003 ◽  
Vol 46 (2) ◽  
pp. 257-267 ◽  
Author(s):  
Scott T. Chapman ◽  
William W. Smith
Keyword(s):  
Class Group ◽  
Subject Classification ◽  
Division Algorithm ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Irreducible Elements ◽  
Complete Set ◽  
Cross Number ◽  
Block Monoids ◽  
Block Monoid

AbstractWe consider the factorization properties of block monoids on $\mathbb{Z}_n$ determined by subsets of the form $S_a=\{\bar{1},\bar{a}\}$. We denote such a block monoid by $\mathcal{B}_a(n)$. In §2, we provide a method based on the division algorithm for determining the irreducible elements of $\mathcal{B}_a(n)$. Section 3 offers a method to determine the elasticity of $\mathcal{B}_a(n)$ based solely on the cross number. Section 4 applies the results of §3 to investigate the complete set of elasticities of Krull monoids with divisor class group $\mathbb{Z}_n$.AMS 2000 Mathematics subject classification: Primary 20M14; 20D60; 13F05

scholarly journals A Theorem About Maximal Cohen–Macaulay Modules

2020 ◽  
Author(s):  
Thomas Polstra
Keyword(s):  
Natural Number ◽  
Regular Ring ◽  
Class Group ◽  
Torsion Subgroup ◽  
Finitely Generated ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Frobenius Endomorphism

Abstract It is shown that for any local strongly $F$-regular ring there exists natural number $e_0$ so that if $M$ is any finitely generated maximal Cohen–Macaulay module, then the pushforward of $M$ under the $e_0$th iterate of the Frobenius endomorphism contains a free summand. Consequently, the torsion subgroup of the divisor class group of a local strongly $F$-regular ring is finite.

scholarly journals The Noether–Lefschetz theorem for the divisor class group

2009 ◽  
Vol 322 (9) ◽  
pp. 3373-3391 ◽  
Author(s):  
G.V. Ravindra ◽  
V. Srinivas
Keyword(s):  
Class Group ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Lefschetz Theorem
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