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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.

Equations for the set of overrings of normal rings and related ring extensions

Mabrouk Ben Nasr, Ali Jaballah (2023)

Czechoslovak Mathematical Journal

We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.

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