local cohomology modules
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Author(s):  
James Lewis

We investigate the rational powers of ideals. We find that in the case of monomial ideals, the canonical indexing leads to a characterization of the rational powers yielding that symbolic powers of squarefree monomial ideals are indeed rational powers themselves. Using the connection with symbolic powers techniques, we use splittings to show the convergence of depths and normalized Castelnuovo–Mumford regularities. We show the convergence of Stanley depths for rational powers, and as a consequence of this, we show the before-now unknown convergence of Stanley depths of integral closure powers. Additionally, we show the finiteness of asymptotic associated primes, and we find that the normalized lengths of local cohomology modules converge for rational powers, and hence for symbolic powers of squarefree monomial ideals.


2021 ◽  
pp. 1-14
Author(s):  
Marzieh Hatamkhani ◽  
Hajar Roshan-Shekalgourabi

2021 ◽  
Vol 3 (1) ◽  
pp. 108-112
Author(s):  
Payman Mahmood Hamaali ◽  
Adil Kadir Jabbar

Let be a commutative Noetherian ring with identity For a non-zero module . We prove that a multiplication primeful module and are I-cofinite and primeful, for each where is an ideal of with . As a consequence, we deduce that, if and are multiplication primeful R- modules, then is primeful. Another result is, for a projective module over an integral domain, admits projective resolution such that each is primeful (faithfully flat).


2021 ◽  
Vol 110 (1-2) ◽  
pp. 100-109
Author(s):  
Nguyen Minh Tri ◽  
Tran Tuan Nam ◽  
Nguyen Thanh Nam

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Alireza Vahidi ◽  
Moharram Aghapournahr ◽  
Elahe Mahmoudi Renani

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