unique factorization
Recently Published Documents


TOTAL DOCUMENTS

275
(FIVE YEARS 6)

H-INDEX

16
(FIVE YEARS 0)

Author(s):  
Daniel Daigle ◽  
Gene Freudenburg ◽  
Takanori Nagamine


Author(s):  
Yangjiang Wei ◽  
Huadong Su ◽  
Linhua Liang

Let [Formula: see text] be the rational filed. For a square-free integer [Formula: see text] with [Formula: see text], we denote by [Formula: see text] the quadratic field. Let [Formula: see text] be the ring of algebraic integers of [Formula: see text]. In this paper, we completely determine the unit group of the quotient ring [Formula: see text] of [Formula: see text] for an arbitrary prime [Formula: see text] in [Formula: see text], where [Formula: see text] has the unique factorization property, and [Formula: see text] is a rational integer.



2021 ◽  
Vol 128 (6) ◽  
pp. 554-558
Author(s):  
Paul Pollack ◽  
Noah Snyder
Keyword(s):  


2021 ◽  
Author(s):  
J. R. Juett ◽  
Christopher Park Mooney ◽  
Rhys D. Roberts


2021 ◽  
pp. 1-25
Author(s):  
J. R. Juett ◽  
Christopher Park Mooney ◽  
Lois W. Ndungu




2020 ◽  
Vol 224 (12) ◽  
pp. 106430
Author(s):  
Gyu Whan Chang ◽  
Andreas Reinhart


2020 ◽  
Vol 27 (03) ◽  
pp. 643-650
Author(s):  
B. Boulayat ◽  
S. El Baghdadi

Let A ⊆ B be an extension of integral domains and Γ a commutative, additive, cancellative, torsion-free monoid with Γ ∩ −Γ = {0}. Let B[Γ] be the semigroup ring of Γ over B and set Γ∗ = Γ\{0}. Then R = A + B[Γ∗] is a subring of B[Γ]. We investigate various factorization properties which are weaker than unique factorization in the domains of the form A + B[Γ∗].



2020 ◽  
Vol 27 (03) ◽  
pp. 369-380
Author(s):  
Gyu Whan Chang ◽  
HwanKoo Kim

Let D be an integral domain, F+(D) (resp., f+(D)) be the set of nonzero (resp., nonzero finitely generated) ideals of D, R1 = f+(D) ∪ {(0)}, and R2 = F+(D) ∪ {(0)}. Then (Ri, ⊕, ⊗) for i = 1, 2 is a commutative semiring with identity under I ⊕ J = I + J and I ⊗ J = IJ for all I, J ∈ Ri. In this paper, among other things, we show that D is a Prüfer domain if and only if every ideal of R1 is a k-ideal if and only if R1 is Gaussian. We also show that D is a Dedekind domain if and only if R2 is a unique factorization semidomain if and only if R2 is a principal ideal semidomain. These results are proved in a more general setting of star operations on D.



Author(s):  
D. D. Anderson ◽  
Ranthony A. C. Edmonds

Given a certain factorization property of a ring [Formula: see text], we can ask if this property extends to the polynomial ring over [Formula: see text] or vice versa. For example, it is well known that [Formula: see text] is a unique factorization domain if and only if [Formula: see text] is a unique factorization domain. If [Formula: see text] is not a domain, this is no longer true. In this paper, we survey unique factorization in commutative rings with zero divisors, and characterize when a polynomial ring over an arbitrary commutative ring has unique factorization.



Sign in / Sign up

Export Citation Format

Share Document