Modules with annihilation property
| Autor: | Rasul Mohammadi, Masoome Zahiri, Ahmad Moussavi |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Ring (mathematics)
Algebra and Number Theory Property (philosophy) Computer Science::Information Retrieval Applied Mathematics 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Local ring Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 020206 networking & telecommunications 02 engineering and technology 01 natural sciences Combinatorics Annihilator Identity (mathematics) 0202 electrical engineering electronic engineering information engineering Computer Science::General Literature Ideal (ring theory) 0101 mathematics Associative property Zero divisor Mathematics |
| Zdroj: | Journal of Algebra and Its Applications. 20:2150126 |
| ISSN: | 1793-6829 0219-4988 |
| DOI: | 10.1142/s0219498821501267 |
| Popis: | Let [Formula: see text] be an associative ring with identity. A right [Formula: see text]-module [Formula: see text] is said to have Property ([Formula: see text]), if each finitely generated ideal [Formula: see text] has a nonzero annihilator in [Formula: see text]. Evans [Zero divisors in Noetherian-like rings, Trans. Amer. Math. Soc. 155(2) (1971) 505–512.] proved that, over a commutative ring, zero-divisor modules have Property ([Formula: see text]). We study and construct various classes of modules with Property ([Formula: see text]). Following Anderson and Chun [McCoy modules and related modules over commutative rings, Comm. Algebra 45(6) (2017) 2593–2601.], we introduce [Formula: see text]-dual McCoy modules and show that, for every strictly totally ordered monoid [Formula: see text], faithful symmetric modules are [Formula: see text]-dual McCoy. We then use this notion to give a characterization for modules with Property ([Formula: see text]). For a faithful symmetric right [Formula: see text]-module [Formula: see text] and a strictly totally ordered monoid [Formula: see text], it is proved that the right [Formula: see text]-module [Formula: see text] is primal if and only if [Formula: see text] is primal with Property ([Formula: see text]). |
| Databáze: | OpenAIRE |
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