Ciro Santilli $$Sponsor Ciro$$ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件 邓家贵、低端人口、西藏骚乱
🔗

# Ring (mathematics)

| 🗖 nosplit | ↑ parent "Group" | words: 276 | descendant words: 1k | descendants: 12
🔗
A group with an extra operation called multiplication which satisfies:
🔗
Unlike addition, that multiplication does not need to satisfy:
If those are also satisfied, then we have a field.
🔗
The simplest example of a ring which is not a full fledged field and with commutative multiplication are the integers. Notably, no inverses exist except for the identity itself and -1. E.g. the inverse of 2 would be 1/2 which is not in the set.
🔗
A polynomial ring is another example with the same properties as the integers.
🔗
The simplest non-commutative ring that is not a field is the set of all 2x2 matrices of real numbers:
• we know that 2x2 matrix multiplication is non-commutative in general
• some 2x2 matrices have a multiplicative inverse, but others don't
Note that is not a ring because you can by addition reach the zero matrix.
🔗
🔗

🔗