prime element (Q2229): Difference between revisions

@@ Property / Freebase ID @@
+/m/0gfh1sw
@@ Property / Freebase ID: /m/0gfh1sw / rank @@
+Normal rank
@@ Property / Freebase ID: /m/0gfh1sw / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / MathWorld ID @@
+PrimeElement
@@ Property / MathWorld ID: PrimeElement / rank @@
+Normal rank
@@ Property / defining formula @@
+ $p\mid ab\land p\nmid a\implies p\mid b$ 
p\mid ab \land p \nmid a \implies p \mid b
@@ Property / defining formula: $p\mid ab\land p\nmid a\implies p\mid b$ / rank @@
+Normal rank
+stated in: MathWorld
MathWorld ID: PrimeElement
@@ Property / subclass of @@
+element
@@ Property / subclass of: element / rank @@
+Normal rank
@@ Property / subclass of: element / qualifier @@
+of: commutative ring
@@ Property / subclass of @@
+irreducible element
@@ Property / subclass of: irreducible element / rank @@
+Normal rank
@@ Property / subclass of: irreducible element / qualifier @@
+valid in place: integral domain
@@ Property / subclass of @@
+non-unit
@@ Property / subclass of: non-unit / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+116335209
@@ Property / Microsoft Academic ID: 116335209 / rank @@
+Normal rank
@@ Property / nLab ID @@
+prime element
@@ Property / nLab ID: prime element / rank @@
+Normal rank
@@ Property / different from @@
+irreducible element
@@ Property / different from: irreducible element / rank @@
+Normal rank
@@ Property / different from @@
+uniformizing parameter
@@ Property / different from: uniformizing parameter / rank @@
+Normal rank
@@ Property / part of @@
+primality in a ring
@@ Property / part of: primality in a ring / rank @@
+Normal rank
@@ Property / OpenAlex ID @@
+C116335209
@@ Property / OpenAlex ID: C116335209 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C116335209 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / Metamath statement ID @@
+df-rprm
@@ Property / Metamath statement ID: df-rprm / rank @@
+Normal rank

Latest revision as of 16:04, 29 July 2024

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)

Language	Label	Description	Also known as
English	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)