ON CLASSICAL WEAKLY PRIME SUBMODULES
Abstract
The aim of this paper is to introduce the concept of classical weakly prime submodules which is the generalization of the notion of weakly classical prime submodules to modules over arbitrary noncommutative rings. We study some properties of classical weakly prime submodules and investigate their structure in different classes of modules. Also, the structure of such submodules of modules over duo rings is completely described. We investigate some properties of classical weakly prime submodules of multiplication modules.
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D. D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math.,
Vol. 29, no. 4, (2003) 831-840.
M. Behboodi, A generalization of Bears lower nilradical for modules, J. Al-
gebra Appl., Vol. 6, no. 2, (2007) 337-353.
M. Behboodi, Classical prime submodules, Ph.D. Thesis, Chamran Univer-
sity, Ahvaz, Iran (2004).
M. Behboodi, On weakly prime radical of modules and semi-compatible mod-
ules, Acta Math. Hungar., Vol. 113, no. 3, (2006) 239-250.
M. Behboodi and H. Koohi, Weakly prime submodules, Vietnam J. Math.,
Vol. 32, (2004) 185-195.
S. Ebrahimi Atani and F. Farzalipour, On weakly prime submodules,
Tamk. J. Math., Vol. 38, no. 3, (2007) 247-252.
Y. Hirano, E. Poon and H. Tsutsui, On rings in which every ideal is
weakly prime, Bull. Korean Math. Soc., Vol. 47, (2010) 1077-1087.
H. Mostafanasab, U. Tekir and K. H. Oral, Weakly classical prime
submodules, Kyungpook Mathematical Journal, Vol. 56, (2016) 1085-1101.
P. Quartararo and H. S. Butts, Finite unions of ideals and modules,
Proc. Amer. Math. Soc., Vol. 52, (1975) 91-96.
A. A. Tuganbaev, Multiplication modules over non-commutative rings,
Sbornik: Mathematics, Vol. 194, (2003) 1837-1864.
DOI: https://doi.org/10.22190/FUMI200906003J
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