0
votes
0answers
10 views

Notations in Oka family definition

Definition. An ideal family $F$ in a ring $R$ with $R \in F$ is said to be an Oka family (strongly Oka family) if, for $a \in R$ and $I$, $A \lhd R$, $(I, a), (I:a) \in F \Rightarrow I \in F$ ...
3
votes
2answers
114 views

What letter should I use to denote an ideal?

In commutative algebra, there seem to be two rather different notational conventions for ideals: either $I,J, \dots$ or $\mathfrak{a}, \mathfrak{b}, \dots$. By itself, it is hardly surprising - after ...
7
votes
3answers
545 views

Is $\lhd$ common notation for “is an ideal of”?

This question is because of this comment. I would like to know if I should refrain from using $\lhd$ for "is an ideal of" in ring-theoretic questions. Is it common enough, or should I explain what it ...
1
vote
1answer
532 views

Notation about sums and direct sums of ideals

Let $A_1,A_2,\dots,A_n$ be a family of (right) ideals. $A_1+A_2+\cdots +A_n$ is the sum of these ideals (it is the smallest ideal containing the $A_i$'s). Another way to denote this sum is ...