منابع مشابه
Completely Prime Ideal Rings and Their Extensions
Let R be a ring and let I 6= R be an ideal of R. Then I is said to be a completely prime ideal of R if R/I is a domain and is said to be completely semiprime if R/I is a reduced ring. In this paper, we introduce a new class of rings known as completely prime ideal rings. We say that a ring R is a completely prime ideal ring (CPI-ring) if every prime ideal of R is completely prime. We say that a...
متن کاملS - Fuzzy Prime Ideal Theorem
The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72
متن کاملT-Rough (Prime, Primary) Ideal and T-Rough Fuzzy (Prime, Primary) Ideal on Commutative Rings
The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...
متن کاملPrime Ideal Theorem for Double Boolean Algebras
Double Boolean algebras are algebras (D,u,t, , ,⊥,>) of type (2, 2, 1, 1, 0, 0). They have been introduced to capture the equational theory of the algebra of protoconcepts. A filter (resp. an ideal) of a double Boolean algebra D is an upper set F (resp. down set I) closed under u (resp. t). A filter F is called primary if F 6= ∅ and for all x ∈ D we have x ∈ F or x ∈ F . In this note we prove t...
متن کاملG-free Colorability and the Boolean Prime Ideal Theorem
We show that the compactness of G-free k-colorability is equivalent to the Boolean prime ideal theorem for any graph G with more than two vertices and any k ≥ 2.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2011
ISSN: 0166-8641
DOI: 10.1016/j.topol.2011.03.012