Integral commutative algebra's definition

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I was reading a text where I found the expression

Take an integral commutative $\mathbb{C}$-algebra.

It' doesn't give a definition so I don't know what it means for $\textbf{integral}$. Now I don't know if it means that the algebra is an integral domain as a ring or if it is integrally closed. Hence I want to ask if there is a standard definition of integral commutative $\mathbb{C}$-algebra.

thanks in advance.