Definition of a Zero Divisor with Examples of Zero Divisors

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Definition of a Zero Divisor with Examples of Zero Divisors
- Examples of zero divisors in Z_m the ring with addition modulo m and multiplication modulo m. Examples are done with Z_8 and Z_4.
- Example of a zero divisor with the Direct Sum of Rings.
- Example of a zero divisor in a matrix ring.

[@mahandratiwari8027]

Very nice Sir

[@TheMathSorcerer]

thanks glad it helped!

[@rakhshandailyas6790]

Excellent explination🙌

[@TheMathSorcerer]

Glad it was helpful!

[@chufuonlinestudy3074]

Thanks a lot sir.

[@TheMathSorcerer]

You are welcome!

[@Lange0716]

How would you find the zero divisors of the Cartesian product of two rings of integers? For instance Z6 x Z8

[@user-uw1ut4ss2q]

The product of (0,x) and (y,0) is alway (0,0) no matter what values x and y have, so the Cartesian product of two ring always has zero divisors.