depth (Q2801): Difference between revisions

@@ Property / subclass of @@
+invariant
@@ Property / subclass of: invariant / rank @@
+Normal rank
@@ Property / Freebase ID @@
+/m/02prpy1
@@ Property / Freebase ID: /m/02prpy1 / rank @@
+Normal rank
@@ Property / Freebase ID: /m/02prpy1 / 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 / defining formula @@
+ $\operatorname {depth} _{I}(M)=\min\{i\colon \operatorname {Ext} ^{i}(R/I,M)\neq 0\}$ 
\operatorname{depth}_I(M)=\min\{i\colon\operatorname{Ext}^i(R/I,M)\neq 0\}
+Normal rank
@@ Property / Encyclopedia of Mathematics article ID @@
+Depth_of_a_module
@@ Property / Encyclopedia of Mathematics article ID: Depth_of_a_module / rank @@
+Normal rank
@@ Property / in defining formula @@
+ $\operatorname {depth}$ 
\operatorname{depth}
@@ Property / in defining formula: $\operatorname {depth}$ / rank @@
+Normal rank
@@ Property / in defining formula: $\operatorname {depth}$ / qualifier @@
+symbol represents: depth
@@ Property / in defining formula @@
+ $M$ 
M
@@ Property / in defining formula: $M$ / rank @@
+Normal rank
@@ Property / in defining formula: $M$ / qualifier @@
+symbol represents: finitely generated module
@@ Property / in defining formula @@
+ $R$ 
R
@@ Property / in defining formula: $R$ / rank @@
+Normal rank
@@ Property / in defining formula: $R$ / qualifier @@
+symbol represents: commutative ring
@@ Property / in defining formula @@
+ $I$ 
I
@@ Property / in defining formula: $I$ / rank @@
+Normal rank
@@ Property / in defining formula: $I$ / qualifier @@
+symbol represents: two-sided ideal
@@ Property / in defining formula @@
+ $/$ 
/
@@ Property / in defining formula: $/$ / rank @@
+Normal rank
@@ Property / in defining formula: $/$ / qualifier @@
+symbol represents: quotient ring
@@ Property / in defining formula @@
+ $\operatorname {Ext}$ 
\operatorname{Ext}
@@ Property / in defining formula: $\operatorname {Ext}$ / rank @@
+Normal rank
@@ Property / in defining formula: $\operatorname {Ext}$ / qualifier @@
+symbol represents: Ext functor