Simple Issue of oh symbol - exact sequences

[Math Amateur]

I am reading Adhikari and Adhikari's (A&A) book, "Basic Modern Algebra with Applications".

I am currently focussed on Section 9.7 Exact Sequences. On page 387, A&A give Theorem 9.7.1.

A&A use symbol in the exact sequences that looks like an oh but I think it should be a zero. They continue this 'mistake' or printing error until the end of the page with Example 9.7(d) where the book reverts to a zero symbol in the exact sequence.

I believe the oh symbol is a typo - I think it should be a zero - can someone please confirm that I am correct ...

Page 387 of A&A follows:View attachment 3627

I would very much appreciate someone confirming that the oh symbol (O) in the above text should be a zero (0) ...

Peter

 

[Opalg]

I think that the authors are using $O$ to denote the $R$-module that consists of a single element $0$ (or you could call the element $0_O$, to denote that it is the zero element of the module $O$). But in the first line of the proof of Theorem 9.7.1, "$\ker f = \{O_M\}$" should surely be "$\ker f = \{0_M\}$": the kernel of $f$ is the submodule of $M$ consisting of the zero element of $M$.

 

[Math Amateur]

I think that the authors are using $O$ to denote the $R$-module that consists of a single element $0$ (or you could call the element $0_O$, to denote that it is the zero element of the module $O$). But in the first line of the proof of Theorem 9.7.1, "$\ker f = \{O_M\}$" should surely be "$\ker f = \{0_M\}$": the kernel of $f$ is the submodule of $M$ consisting of the zero element of $M$.

Thanks so much Opalg ... appreciate the clarification ... most helpful ...

Peter