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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 25th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe entry used to start out with the line "not to be confused with [[neutral element]]". This was rather suboptimal. I have removed that sentence and instead expanded the Idea-section to read now as follows: > Considering a [[ring]] $R$, then by _the unit element_ one usually means the [[neutral element]] $1 \in R$ with respect to [[multiplication]]. This is the sense of "unit" in terms such as [[nonunital ring]]. > But more generally _a unit element_ in a unital (!) ring is any element that has an [[inverse element]] under [[multiplication]]. > This concept generalizes beyond [[rings]], and this is what is discussed in the following. <a href="https://ncatlab.org/nlab/revision/diff/unit/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/unit/12">v12</a>, <a href="https://ncatlab.org/nlab/show/unit">current</a>

   The entry used to start out with the line “not to be confused with neutral element”. This was rather suboptimal. I have removed that sentence and instead expanded the Idea-section to read now as follows:

   Considering a ring $R$, then by the unit element one usually means the neutral element $1 \in R$ with respect to multiplication. This is the sense of “unit” in terms such as nonunital ring.

   But more generally a unit element in a unital (!) ring is any element that has an inverse element under multiplication.

   This concept generalizes beyond rings, and this is what is discussed in the following.

   diff, v12, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 20th 2021
   • (edited Sep 20th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have hyperlinked *[[unit of measurement]]* ([here](https://ncatlab.org/nlab/show/unit#UnitsOfMeasurement)) and made that redirect to *[[physical unit]]*. <a href="https://ncatlab.org/nlab/revision/diff/unit/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/unit/15">v15</a>, <a href="https://ncatlab.org/nlab/show/unit">current</a>

   I have hyperlinked unit of measurement (here) and made that redirect to physical unit.

   diff, v15, current

3. • CommentRowNumber3.
   • CommentAuthornLab edit announcer
   • CommentTimeSep 24th 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexGiven a response to the query for the non-commutative case Giovanni Giacalone <a href="https://ncatlab.org/nlab/revision/diff/unit/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/unit/20">v20</a>, <a href="https://ncatlab.org/nlab/show/unit">current</a>

   Given a response to the query for the non-commutative case

   Giovanni Giacalone

   diff, v20, current

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeSep 24th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAdded All units in a unital ring form a group, the group of units. <a href="https://ncatlab.org/nlab/revision/diff/unit/22">diff</a>, <a href="https://ncatlab.org/nlab/revision/unit/22">v22</a>, <a href="https://ncatlab.org/nlab/show/unit">current</a>

   Added

   All units in a unital ring form a group, the group of units.

   diff, v22, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 25th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded cross-link with *[[group of units]]* <a href="https://ncatlab.org/nlab/revision/diff/unit/23">diff</a>, <a href="https://ncatlab.org/nlab/revision/unit/23">v23</a>, <a href="https://ncatlab.org/nlab/show/unit">current</a>

   added cross-link with group of units

   diff, v23, current