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Abstract Algebra
Let R be any ring whose additive group is torsion-free. Show (without using Amitsur’s Theorem) that J = rad R[t] <> 0 implies that R ∩ J <> 0.
Abstract Algebra
Suppose R is a simple ring which has a minimal left ideal. Then soc(RR) <> 0 and so soc(RR) = R. This means that RR is a semisimple module, so R is a semisimple ring.
Abstract Algebra
Give a proof for the fact that if R is a simple ring which has a minimal left ideal, then R is a semisimple ring.
Abstract Algebra
Show that for any ring R, soc(R) (= sum of all minimal left ideals of R) is an ideal of R.
Abstract Algebra
Let R be a ring possibly without an identity. Show that a left identity for R need not be a right identity.
Abstract Algebra
Let p be a fixed prime. Show that any ring (with identity) of order p^2 is commutative.
Abstract Algebra
Test teste s
Abstract Algebra
Test question_test
Abstract Algebra
Given the demand function Pd=25- 2Q and the supply function Ps= 2Q+1.Asssuming
pure competition, find the consumers’ surplus, producers’ surplus and interpret the total
of consumers’ surplus and producers’ surplus
pure competition, find the consumers’ surplus, producers’ surplus and interpret the total
of consumers’ surplus and producers’ surplus
Abstract Algebra
What is the equation for (6,1)
