Weakly unique factorization modules

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Abstract

In this work we give the definition of weakly prime element of a module. Therefore we give a new definition of factorization in a module, which is called weakly factorization. So we call a module weakly unique factorization module if all elements have a weakly factorization which is unique. We give the relation between weakly prime elements and weakly prime submodules. Then we characterize such weakly unique factorization modules.

Related Papers

• → On the factorization of polynomials(1969)5 cited
• → Factorization of Prime Ideal Extensions in Dedekind Domains(1995)1 cited
• → Nonunique Factorization in Subsemigroups of Semigroups with Unique Prime Factorization(1980)1 cited
• → Nonunique Factorization in Subsemigroups of Semigroups with Unique Prime Factorization(1980)1 cited
• Conditions of Prime Elements and Properties of Factorization of Some Integral Domains(2000)