Strongly Prime Radicals and S-Primary Ideals in Posets

Author(s):  
J. Catherine Grace John
Keyword(s):  
2018 ◽  
Vol 1 (21) ◽  
pp. 415-438
Author(s):  
Amer Shamil Abdulrhman

In this paper we study covering ideals by Cosets of primary ideals and we get a generalized the primary avoidance theorem in the rings which it has been


1993 ◽  
Vol 78 (1) ◽  
pp. 201-221 ◽  
Author(s):  
Robert Gilmer ◽  
William Heinzer

2021 ◽  
Author(s):  
Kothuru Bhagyalakshmi ◽  
V. Amarendra Babu
Keyword(s):  

1988 ◽  
Vol 53 (1) ◽  
pp. 284-293 ◽  
Author(s):  
T. G. Kucera

This is the second of two papers based on Chapter V of the author's Ph.D. thesis [K1]. For acknowledgements please refer to [K3]. In this paper I apply some of the ideas and techniques introduced in [K3] to the study of a very specific example. I obtain an upper bound for the positive Deissler rank of an injective module over a commutative Noetherian ring in terms of Krull dimension. The problem of finding lower bounds is vastly more difficult and is not addressed here, although I make a few comments and a conjecture at the end.For notation, terminology and definitions, I refer the reader to [K3]. I also use material on ideals and injective modules from [N] and [Ma]. Deissler's rank was introduced in [D].For the most part, in this paper all modules are unitary left modules over a commutative Noetherian ring Λ but in §1 I begin with a few useful results on totally transcendental modules and the relation between Deissler's rank rk and rk+.Recall that if P is a prime ideal of Λ, then an ideal I of Λ is P-primary if I ⊂ P, λ ∈ P implies that λn ∈ I for some n and if λµ ∈ I, λ ∉ P, then µ ∈ I. The intersection of finitely many P-primary ideals is again P-primary, and any P-primary ideal can be written as the intersection of finitely many irreducible P-primary ideals since Λ is Noetherian. Every irreducible ideal is P-primary for some prime ideal P. In addition, it will be important to recall that if P and Q are prime ideals, I is P-primary, J is Q-primary, and J ⊃ I, then Q ⊃ P. (All of these results can be found in [N].)


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