All rings are commutative and unital
Q1: what means notation $A\cong A_1\times\ldots\times A_n?$ Is it true that elements of $A_1\times\ldots\times A_n$ are collection of elements of $A_1,\ldots ,A_n$ with termwise multiplication and addition? What is the difference between $A_1\times\ldots\times A_n$ and $A_1\oplus\ldots\oplus A_n?$
Q2: Let's $\{\mathfrak{m}_i\}_{i\in I}$ is the set of all maximal ideals of ring $A$. Is it true that $\cup_{i\in I}\mathfrak{m}_i$ consists of all non-invertible elements and $A-\{\mathfrak{m}_i\}_{i\in I}$ consists of all invertible elements?
Thanks a lot!