# Ring detail

## Name: $T_n(k)$: the upper triangular matrix ring over a field

Description: The ring of $n \times n$ matrices over a countably infinite field $k$ whose entries below the diagonal are zero.

Keywords matrix ring

Reference(s):

• (Citation needed)

• Legend
• = has the property
• = does not have the property
• = information not in database
Name Measure
cardinality $\aleph_0$
composition length left: $n(n+1)/2$right: $n(n+1)/2$
global dimension left: 1right: 1
Krull dimension (classical) 0

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