# Ring detail

## Name: Right-not-left Kasch ring

Description: Let $F_2$ be the field of two elements, and $R$ be the subring of matrices in $M_4(F_2)$ of the form $\begin{bmatrix} a&0&b&c\\ 0&a&0&d\\ 0&0&a&0\\ 0&0&0&e\end{bmatrix}$

Notes: The field does not have to be finite for the asymmetry of Kasch property: it can be any division ring.

Keywords matrix ring subring

Reference(s):

• T.-Y. Lam. Lectures on modules and rings. (2012) @ p 281

Legend
• = has the property
• = does not have the property
• = information not in database
Name Measure
cardinality 32
composition length left: 6right: 6
Krull dimension (classical) 0

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