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Is the following statement is True /false

A subring of an integral domain is an integral domain

my answer : see the image here there are 2 definition

enter image description here

According to gallian books Its is false But according to maths online it is True

Im confusion which definition i have to accepts, either gallian or maths online

Pliz help me...

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  • $\begingroup$ The picture you posted has no definitions on it. Maybe you could clarify which assumptions are made in each text. $\endgroup$
    – qualcuno
    Jul 23, 2018 at 8:32
  • $\begingroup$ Ok, and as for Gallian's definition? $\endgroup$
    – qualcuno
    Jul 23, 2018 at 8:34
  • $\begingroup$ For gallian books see page no 256 $\endgroup$
    – jasmine
    Jul 23, 2018 at 8:35
  • $\begingroup$ The difference is that Gallian for some reason allows subrings of integral domains which are not subrings when seen as unital rings. $\endgroup$
    – Tobias Kildetoft
    Jul 23, 2018 at 8:35
  • $\begingroup$ @ Tobias okk that mean Gallian is Right $\endgroup$
    – jasmine
    Jul 23, 2018 at 8:39

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