A remark on arithmetical rings

2021 ◽  
Vol 15 (4) ◽  
pp. 259-264
Author(s):  
Majid M. Ali
Keyword(s):  
Arithmetical Rings

scholarly journals Arithmetical rings satisfy the radical formula

2012 ◽  
Vol 4 (2) ◽  
pp. 293-296 ◽  
Author(s):  
Anand Parkash
Keyword(s):  
Arithmetical Rings

Completely Arithmetical Rings

2014 ◽  
Vol 42 (9) ◽  
pp. 4047-4054 ◽  
Author(s):  
Xinmin Lu ◽  
Jason Greene Boynton
Keyword(s):  
Arithmetical Rings

Arithmetical Rings

2021 ◽  
Vol 258 (2) ◽  
pp. 129-198
Author(s):  
A. A. Tuganbaev
Keyword(s):  
Arithmetical Rings

Some Properties of Completely Arithmetical Rings

2016 ◽  
Vol 23 (01) ◽  
pp. 83-88
Author(s):  
Xinmin Lu
Keyword(s):  
Positive Integer ◽  
Proper Ideal ◽  
Strongly Irreducible ◽  
Arithmetical Rings

In this paper, we introduce the concept of completely arithmetical rings and investigate their properties. In particular, we prove that if R is a completely arithmetical ring with J(R)=0, then K0(R) ≅ ℤn for some positive integer n. We also show that such a ring is precisely a ring in which every proper ideal can be written uniquely as a product of finitely many distinct completely strongly irreducible ideals.

Pullbacks of Arithmetical Rings

2007 ◽  
Vol 35 (9) ◽  
pp. 2671-2684 ◽  
Author(s):  
Jason Boynton
Keyword(s):  
Arithmetical Rings
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