Abstract—In this paper, the possibility of obtaining certain direct sum decompositions, for a given complete two-dimensional behavior, are investigated and proved to be equivalent to the zero skew-primeness property of suitable matrix pairs. Some known decomposition theorems for two-dimensional complete behaviors are later obtained as simple corollaries of this general result.
A note on the direct sum decomposition of two-dimensional behaviors
BISIACCO, MAURO;VALCHER, MARIA ELENA
2001
Abstract
Abstract—In this paper, the possibility of obtaining certain direct sum decompositions, for a given complete two-dimensional behavior, are investigated and proved to be equivalent to the zero skew-primeness property of suitable matrix pairs. Some known decomposition theorems for two-dimensional complete behaviors are later obtained as simple corollaries of this general result.
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