scholarly journals Uniform Dimension Results for the Brownian Sheet

1989 ◽  
Vol 17 (4) ◽  
pp. 1454-1462 ◽  
Author(s):  
T. S. Mountford
Keyword(s):  
Brownian Sheet ◽  
Uniform Dimension

On commutative rings with uniserial dimension

2014 ◽  
Vol 14 (01) ◽  
pp. 1550008 ◽  
Author(s):  
A. Ghorbani ◽  
Z. Nazemian
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
Artinian Rings ◽  
Uniform Dimension ◽  
Uniserial Modules

In this paper, we define and study a valuation dimension for commutative rings. The valuation dimension is a measure of how far a commutative ring deviates from being valuation. It is shown that a ring R with valuation dimension has finite uniform dimension. We prove that a ring R is Noetherian (respectively, Artinian) if and only if the ring R × R has (respectively, finite) valuation dimension if and only if R has (respectively, finite) valuation dimension and all cyclic uniserial modules are Noetherian (respectively, Artinian). We show that the class of all rings of finite valuation dimension strictly lies between the class of Artinian rings and the class of semi-perfect rings.

On the Increments of the Brownian Sheet

2006 ◽  
pp. 269-278
Author(s):  
José R. León ◽  
Oscar Rondón
Keyword(s):  
Brownian Sheet
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