scholarly journals MAXIMAL CHAINS OF CLOSED PRIME IDEALS FOR DISCONTINUOUS ALGEBRA NORMS ON

2012 ◽  
Vol 112A (2) ◽  
pp. 101-115
Author(s):  
J. Esterle
Keyword(s):  
Prime Ideals ◽  
Maximal Chains

scholarly journals Representation of certain classes of distributive lattices by sections of sheaves

1980 ◽  
Vol 3 (3) ◽  
pp. 461-476
Author(s):  
U. Maddana Swamy ◽  
P. Manikyamba
Keyword(s):  
Distributive Lattice ◽  
Main Tool ◽  
Distributive Lattices ◽  
Prime Ideals ◽  
Post Algebra ◽  
Boolean Space ◽  
Bounded Distributive Lattice ◽  
Maximal Chains

Epstein and Horn ([6]) proved that a Post algebra is always aP-algebra and in aP-algebra, prime ideals lie in disjoint maximal chains. In this paper it is shown that aP-algebraLis a Post algebra of ordern≥2, if the prime ideals ofLlie in disjoint maximal chains each withn−1elements. The main tool used in this paper is that every bounded distributive lattice is isomorphic with the lattice of all global sections of a sheaf of bounded distributive lattices over a Boolean space. Also some properties ofP-algebras are characterized in terms of the stalks.

Finite maximal chains of commutative rings

2014 ◽  
Vol 14 (01) ◽  
pp. 1450075 ◽  
Author(s):  
Ahmed Ayache ◽  
David E. Dobbs
Keyword(s):  
Maximal Chain ◽  
Commutative Rings ◽  
Prime Ideals ◽  
Quotient Field ◽  
One Dimensional ◽  
Normal Pair ◽  
Intermediate Ring ◽  
Additional Domain ◽  
Maximal Chains ◽  
Dimensional Domain

Let R ⊆ S be a unital extension of commutative rings, with [Formula: see text] the integral closure of R in S, such that there exists a finite maximal chain of rings from R to S. Then S is a P-extension of R, [Formula: see text] is a normal pair, each intermediate ring of R ⊆ S has only finitely many prime ideals that lie over any given prime ideal of R, and there are only finitely many [Formula: see text]-subalgebras of S. Each chain of rings from R to S is finite if dim (R) = 0; or if R is a Noetherian (integral) domain and S is contained in the quotient field of R; or if R is a one-dimensional domain and S is contained in the quotient field of R; but not necessarily if dim (R) = 2 and S is contained in the quotient field of R. Additional domain-theoretic applications are given.

N-ideals of commutative rings

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2933-2941 ◽  
Author(s):  
Unsal Tekir ◽  
Suat Koc ◽  
Kursat Oral
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
Proper Ideal ◽  
Prime Ideals ◽  
Nonzero Identity

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ? I with a ? ?0, then b ? I for every a,b ? R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.

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