The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Cale Bases in Algebraic Orders”

Uppers to zero in R [ x ] and almost principal ideals

Keivan Borna, Abolfazl Mohajer-Naser (2013)

Czechoslovak Mathematical Journal

Similarity:

Let R be an integral domain with quotient field K and f ( x ) a polynomial of positive degree in K [ x ] . In this paper we develop a method for studying almost principal uppers to zero ideals. More precisely, we prove that uppers to zero divisorial ideals of the form I = f ( x ) K [ x ] ∩ R [ x ] are almost principal in the following two cases: – J , the ideal generated by the leading coefficients of I , satisfies J - 1 = R . – I - 1 as the R [ x ] -submodule of K ( x ) is of finite type. Furthermore we prove that for I = f ( x ) K [ x ] ∩ R [ x ] we have: – I - 1 ∩ K [ x ] = ( I : K ( x ) I ) . – If there exists...

Star operations in extensions of integral domains

David F. Anderson, Said El Baghdadi, Muhammad Zafrullah (2010)

Actes des rencontres du CIRM

Similarity:

An extension D ⊆ R of integral domains is t - (resp., t -) if ( I R ) - 1 = ( I - 1 R ) v (resp., ( I R ) v = ( I v R ) v ) for every nonzero finitely generated fractional ideal I of D . We show that strongly t -compatible implies t -compatible and give examples to show that the converse does not hold. We also indicate situations where strong t -compatibility and its variants show up naturally. In addition, we study integral domains D such that D ⊆ R is strongly t -compatible (resp., t -compatible) for every overring R of D . ...

Characterization of irreducible polynomials over a special principal ideal ring

Brahim Boudine (2023)

Mathematica Bohemica

Similarity:

A commutative ring R with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length e is the index of nilpotency of its maximal ideal. In this paper, we show a characterization of irreducible polynomials over a SPIR of length 2 . Then, we give a sufficient condition for a polynomial to be irreducible over a SPIR of any length e .

On the ring of p -integers of a cyclic p -extension over a number field

Humio Ichimura (2005)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let p be a prime number. A finite Galois extension N / F of a number field F with group G has a normal p -integral basis ( p -NIB for short) when 𝒪 N ′ is free of rank one over the group ring 𝒪 F ′ [ G ] . Here, 𝒪 F ′ = 𝒪 F [ 1 / p ] is the ring of p -integers of F . Let m = p e be a power of p and N / F a cyclic extension of degree m . When ζ m ∈ F × , we give a necessary and sufficient condition for N / F to have a p -NIB (Theorem 3). When ζ m ∉ F × and p ∤ [ F ( ζ m ) : F ] , we show that N / F has a p -NIB if and only if N ( ζ m ) / F ( ζ m ) has a p -NIB (Theorem 1). When p divides [ F ( ζ m ) : F ] , we show that this...

On wsq-primary ideals

Emel Aslankarayiğit Uğurlu, El Mehdi Bouba, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

Similarity:

We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let R be a commutative ring with a nonzero identity and Q a proper ideal of R . The proper ideal Q is said to be a weakly strongly quasi-primary ideal if whenever 0 ≠ a b ∈ Q for some a , b ∈ R , then a 2 ∈ Q or b ∈ Q . Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero...

Making sense of capitulation: reciprocal primes

David Folk (2016)

Acta Arithmetica

Similarity:

Let ℓ be a rational prime, K be a number field that contains a primitive ℓth root of unity, L an abelian extension of K whose degree over K, [L:K], is divisible by ℓ, a prime ideal of K whose ideal class has order ℓ in the ideal class group of K, and a any generator of the principal ideal ℓ . We will call a prime ideal of K ’reciprocal to ’ if its Frobenius element generates G a l ( K ( a ℓ ) / K ) for every choice of a . We then show that becomes principal in L if and only if every reciprocal prime is not...