Chain tensor products and interval effect algebras |
| |
Authors: | Stanley Gudder |
| |
Institution: | (1) Department of Mathematics and Computer Science, University of Denver, 80208 Denver, Colorado |
| |
Abstract: | Weak and strongn-doublings (n∈N) are defined for an effect algebraP and the concept of a normal interval algebra is introduced. It is shown that the following statements are equivalent: (1)
There is a morphism fromP into an interval algebra. (2)P admits a tensor product with every finite chain. (3)P has a weakn-doubling for everyn∈N. Moreover, the following are equivalent: (4)P is a normal interval algebra. (5)P admits a strong tensor product with every chain of length 2
n
,n∈N. (6)P has a strongn-doubling for everyn∈N. Finally, it is shown that ifP possesses an order-determining set of states, thenP is a normal interval algebra. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|