QUIZ Â Â Â Â Â Â Â Welcome to the Quiz on Current Affairs! Test your knowledge on a variety of topics with our engaging and fun quiz. This interactive quiz application presents you with a series of multiple-choice questions covering a range of subjects, from geography and literature to science and history. Â […]
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Prove that the characteristic of a finite ring ( mathcal{R} ) with no zero divisors is a prime number. Solution: Let ((mathcal{R}, +, cdot)) is finite ring having no divisors of zero. Therefoer Char (mathcal{R}=n.) is finite since the characteristic of a finite ring is finite. Let Char (mathcal{R}=n.) To prove, (n) is a prime.
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Prove that the characteristic of a finite ring ( mathcal{R} ) is finite and it is a divisor of ( |mathcal{R}|) where ( |mathcal{R}|) denotes the number of elements of ( mathcal{R}). Solution: Let ((mathcal{R}, +, cdot)) is finite ring. (colorbox{yellow}{First Part}) To prove, Char (mathcal{R}) is finite.(\) Since, by definition, the characteristic of a
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