Terminology in Kaplansky's book In page 3 of the book Commutative Ring by Irving Kaplansky, the author states that: 

Let $R$ be any commutative ring, $A$ any nonzero $R$-module. The prime ideals maximal within the zero-divisor on $A$ are called the maximal primes  of $A$. 

I'm looking for nowaday name of the terminology maximal primes. 
Thank you.
 A: I'm gonna list a few definitions in the modern language for my own sanity. The notation of $A$ for an $R$-module throws me off my game too much, so let me use $M$ instead. So the hypothesis is: $R$ is a commutative ring, $M$ is an $R$-module.
Definition: Let $a\in R$. We say $a$ is $M$-regular if the $R$-linear multiplication map $M\xrightarrow{a}M$ is injective. We call $a$ a zero-divisor of $M$ otherwise.
Definition: An associated prime of $M$ is a prime ideal $\mathfrak{p}\subset R$ such that $\mathfrak{p}=\mathrm{Ann}(x)$ for some $x\in M$. The set of associated primes of $M$ is denoted by $\mathrm{Ass}(M)$.
Proposition: Let $\mathscr{S}$ be the set of all ideals of $R$ such that $\mathfrak{a}\in \mathscr{S}$ iff $\mathfrak{a}=\mathrm{Ann}(x)$ for some $0\neq x\in M$. An ideal $\mathfrak{p}$ which is maximal in $\mathscr{S}$ is a prime ideal. 
If $\mathfrak{p}$ is an associated prime of $M$, then $\mathfrak{p}\in \mathscr{S}$, i.e. $\mathrm{Ass}(M)\subset \mathscr{S}$. At the same time let $Z(M)$ be the set of zero-divisors of $M$. Then $Z(M)=\bigcup \mathscr{S}$ is the union of all elements of $\mathscr{S}$. As a result what you are looking for, in this language, is simply a "maximal associated prime" of $M$.
Side note: If $R$ is furthermore Noetherian, then $\mathrm{Ass}(M)\neq \emptyset$ iff $M\neq 0$. In that case any ideal $\mathrm{Ann}(x)\in \mathscr{S}$ is contained in a maximal associated prime $\mathfrak{p}\in \mathrm{Ass}(M)$. This results in
$$
Z(M)=\bigcup_{\mathfrak{p}\in \mathrm{Ass}(M)}\mathfrak{p}
$$
All of this aside, however, I don't think the terminology of "maximal associated prime" is a very popular one in the literature. People just don't call this concept with any special name most of the time.
