RINGS WHOSE PRIME RADICALS ARE COMPLETELY PRIME
نویسندگان
چکیده
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 کاملUnitary Strongly Prime Rings and Related Radicals
A unitary strongly prime ring is defined as a prime ring whose central closure is simple with identity element. The class of unitary strongly prime rings is a special class of rings and the corresponding radical is called the unitary strongly prime radical. In this paper we prove some results on unitary strongly prime rings. The results are applied to study the unitary strongly prime radical of...
متن کاملPrime Decompositions of Radicals in Polynomial Rings
In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...
متن کاملPrime Radicals of Skew Laurent Polynomial Rings
Let R be a ring with an automorphism σ. An ideal I of R is σ-ideal of R if σ(I) = I. A proper ideal P of R is σ-prime ideal of R if P is a σ-ideal of R and for σ-ideals I and J of R, IJ ⊆ P implies that I ⊆ P or J ⊆ P . A proper ideal Q of R is σ-semiprime ideal of Q if Q is a σ-ideal and for a σ-ideal I of R, I2 ⊆ Q implies that I ⊆ Q. The σ-prime radical is defined by the intersection of all ...
متن کاملPartitions whose parts are pairwise relatively prime
The following problem arose in connection with our research in statistical group theory: estimate a, := the number of partitions of n into parts that are pairwise relatively prime. This differs from most problems in the theory of partitions because of the complicated relationship between the part sixes. We obtain an asymptotic formula for log a,, but leave open the challenging task of obtaining...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2005
ISSN: 1225-1763
DOI: 10.4134/ckms.2005.20.3.457