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Elasticity of A + XB[X] when A ⊂ B is a minimal extension of integral domains

Ahmed Ayache, Hanen Monceur (2011)

Colloquium Mathematicae

We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.

Elasticity of factorizations in atomic monoids and integral domains

Franz Halter-Koch (1995)

Journal de théorie des nombres de Bordeaux

For an atomic domain R , its elasticity ρ ( R ) is defined by : ρ ( R ) = sup { m / n u 1 u m = v 1 v n for irreducible u j , v i R } . We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants μ m ( R ) defined by : μ m ( R ) = sup { n u 1 u m = u 1 v n for irreducible u j , v i R } . As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants μ m and ρ for monoids and integral domains which are of independent interest.

Endomorphism algebras over large domains

Rüdiger Göbel, Simone Pabst (1998)

Fundamenta Mathematicae

The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain

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