scholarly journals Divisibility properties in semigroup rings.

1974 ◽  
Vol 21 (1) ◽  
pp. 65-86 ◽  
Author(s):  
Robert Gilmer ◽  
Tom Parker
Keyword(s):  
Semigroup Rings ◽  
Divisibility Properties

Divisibility properties of twisted semigroup rings

2019 ◽  
Vol 48 (3) ◽  
pp. 1191-1200
Author(s):  
Gyu Whan Chang ◽  
Dong Yeol Oh
Keyword(s):  
Semigroup Rings ◽  
Divisibility Properties

Divisibility Properties of Graded Domains

1982 ◽  
Vol 34 (1) ◽  
pp. 196-215 ◽  
Author(s):  
D. D. Anderson ◽  
David F. Anderson
Keyword(s):  
Integral Domain ◽  
Homogeneous Element ◽  
Carry Over ◽  
Divisibility Properties ◽  
Krull Domains

Let R = ⊕α∊гRα be an integral domain graded by an arbitrary torsionless grading monoid Γ. In this paper we consider to what extent conditions on the homogeneous elements or ideals of R carry over to all elements or ideals of R. For example, in Section 3 we show that if each pair of nonzero homogeneous elements of R has a GCD, then R is a GCD-domain. This paper originated with the question of when a graded UFD (every homogeneous element is a product of principal primes) is a UFD. If R is Z+ or Z-graded, it is known that a graded UFD is actually a UFD, while in general this is not the case. In Section 3 we consider graded GCD-domains, in Section 4 graded UFD's, in Section 5 graded Krull domains, and in Section 6 graded π-domains.

scholarly journals FP-injective semirings, semigroup rings and Leavitt path algebras

2016 ◽  
Vol 45 (5) ◽  
pp. 1893-1906 ◽  
Author(s):  
Marianne Johnson ◽  
Tran Giang Nam
Keyword(s):  
Semigroup Rings ◽  
Path Algebras ◽  
Leavitt Path Algebras

Divisibility Properties of Integers x, k Satisfying 1 k + ⋯+ (x - 1) k = x k

1994 ◽  
Vol 63 (208) ◽  
pp. 799 ◽  
Author(s):  
P. Moree ◽  
H. J. J. Te Riele ◽  
J. Urbanowicz
Keyword(s):  
Divisibility Properties

Dualizing Complexes of Affine Semigroup Rings

1990 ◽  
Vol 322 (2) ◽  
pp. 561 ◽  
Author(s):  
Uwe Schafer ◽  
Peter Schenzel
Keyword(s):  
Semigroup Rings ◽  
Affine Semigroup ◽  
Dualizing Complexes

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

Coefficient rings in isomorphic semigroup rings

1985 ◽  
Vol 13 (8) ◽  
pp. 1789-1809 ◽  
Author(s):  
Robert Gilmer ◽  
Eugene Spiegel
Keyword(s):  
Semigroup Rings
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