prime element
nonzero, non-unit element p in a commutative ring R such that, whenever p divides ab for some a and b in R, then p divides a or p divides b (or both)
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prime element
Summary
prime element ranks in the top 2% of general entities by monthly Wikipedia readership (31 views/month).[1]
Key Facts
- prime element's subclass of is recorded as element[2].
- prime element's subclass of is recorded as irreducible element[3].
- prime element's subclass of is recorded as non-unit[4].
- prime element's part of is recorded as primality in a ring[5].
- prime element's Freebase ID is recorded as /m/0gfh1sw[6].
- prime element's different from is recorded as irreducible element[7].
- prime element's different from is recorded as uniformizing parameter[8].
- prime element's defining formula is recorded as p\mid ab \land p \nmid a \implies p \mid b[9].
- prime element's MathWorld ID is recorded as PrimeElement[10].
- prime element's nLab ID is recorded as prime element[11].
- prime element's maintained by WikiProject is recorded as WikiProject Mathematics[12].
- prime element's Microsoft Academic ID is recorded as 116335209[13].
- prime element's OpenAlex ID is recorded as C116335209[14].
- prime element's Metamath statement ID is recorded as df-rprm[15].
Why It Matters
prime element ranks in the top 2% of general entities by monthly Wikipedia readership (31 views/month).[1] It has Wikipedia articles in 14 language editions, a strong signal of global cultural recognition.[16]