PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS

• Tipo: Artigo em Revista Científica Internacional
• Data: 2005

Autores

Christian Lomp (Autor) FCUP

Revista

Título: Journal of Algebra and its Applications

Vol. 4 Nº 1

Páginas: 77-97

ISSN: 0219-4988

Editora: World Scientific

Indexação

ISI Web of Knowledge - 13 Citações

ISI Web of Science

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

CORDIS: Ciências Físicas > Matemática > Álgebra

Outras Informações

ID Authenticus: P-00M-DFA

DOI: 10.1142/s0219498805001022

Resumo (PT): Primeness on modules can be defined by prime elements in a suitable partially ordered groupoid. Using a product on the lattice of submodules L(M) of a module M defined in [3] we revise the concept of prime modules in this sense. Those modules M for which L(M) has no nilpotent elements have been studied by Jirasko and they coincide with Zelmanowitz’ “weakly compressible” modules. In particular we are interested in representing weakly compressible modules as a subdirect product of “prime” modules in a suitable sense. It turns out that any weakly compressible module is a subdirect product of prime modules (in the sense of Kaplansky). Moreover if M is a self-projective module, then M is weakly compressible if and only if it is a subdirect product of prime modules (in the sense of Bican et al.). An application to Hopf actions is given.

Abstract (EN): Primeness on modules can be defined by prime elements in a suitable partially ordered groupoid. Using a product on the lattice of submodules (M) of a module M defined in [3] we revise the concept of prime modules in this sense. Those modules M for which (M) has no nilpotent elements have been studied by Jirasko and they coincide with Zelmanowitz' "weakly compressible" modules. In particular we are interested in representing weakly compressible modules as a subdirect product of "prime" modules in a suitable sense. It turns out that any weakly compressible module is a subdirect product of prime modules (in the sense of Kaplansky). Moreover if M is a self-projective module, then M is weakly compressible if and only if it is a subdirect product of prime modules (in the sense of Bican et al.). An application to Hopf actions is given.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 21