Behboodi, M., Jahani-Nezhad, R., Naderi, M. (2011). Classical quasi-primary submodules. Bulletin of the Iranian Mathematical Society, 37(No. 4), 51-71.
M. Behboodi; R. Jahani-Nezhad; M. H. Naderi. "Classical quasi-primary submodules". Bulletin of the Iranian Mathematical Society, 37, No. 4, 2011, 51-71.
Behboodi, M., Jahani-Nezhad, R., Naderi, M. (2011). 'Classical quasi-primary submodules', Bulletin of the Iranian Mathematical Society, 37(No. 4), pp. 51-71.
Behboodi, M., Jahani-Nezhad, R., Naderi, M. Classical quasi-primary submodules. Bulletin of the Iranian Mathematical Society, 2011; 37(No. 4): 51-71.
Receive Date: 23 August 2009,
Revise Date: 14 April 2010,
Accept Date: 14 April 2010
Abstract
In this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over Noetherian rings are proved. Moreover, we show that this decomposition and the decomposition into classical primary submodules are the same when $R$ is a domain with ${rm dim}(R)leq 1$.
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