Answer to Question #175838 in Abstract Algebra for Barbie

Question #175838

Find the zero divisors of R × Z2 × Z4

1
Expert's answer
2021-03-29T14:16:58-0400

We remind that the zero divisor is an element "a\\in X={\\mathbb{R}}\\times{\\mathbb{Z}}_2\\times{\\mathbb{Z}}_4" satisfying "ax=0" with some nonzero "x\\in X". The only nonzero divisor of "\\mathbb{R}" is . "\\mathbb{Z}_2" and "\\mathbb{Z}_4" are the following groups: "\\mathbb{Z}_2=\\{0,1\\}" and "\\mathbb{Z}_4=\\{0,1,2,3\\}". For any nonzero "x" from the groups there is "a" satisfying: "a+x=0" except 0. Thus, we receive the following zero divisors: "0\\times(\\mathbb{Z}_2\\setminus\\{0\\})\\times(\\mathbb{Z}_4\\setminus\\{0\\})"


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