
Exercises 5 5.1. Let A be an abelian group. Set A ∗ = HomZ(A,Q/Z
... 5.3. Let A, B, C be modules over a commutative ring R. (a) The set L (A, B; C) of all bilinear maps A × B → C is an R-module with (f + g)(a, b) = f (a, b) + g(a, b), and (rf )(a, b) = rf (a, b). (b) Each one of the following R-modules is isomorphic to L (A, B; C): N i. HomR (A R B, C); ii. HomR (A, ...
... 5.3. Let A, B, C be modules over a commutative ring R. (a) The set L (A, B; C) of all bilinear maps A × B → C is an R-module with (f + g)(a, b) = f (a, b) + g(a, b), and (rf )(a, b) = rf (a, b). (b) Each one of the following R-modules is isomorphic to L (A, B; C): N i. HomR (A R B, C); ii. HomR (A, ...
Lecture 22 Notes
... 1. Why is equationsal reasoning important? The standard presentation of recursive functions is equation based. Also note Barendregt’s account of the lambda calculus is based on equational logic with distinct equalities, ≡, =α , =β . But presenting computation rules as equations is a bit misleading. ...
... 1. Why is equationsal reasoning important? The standard presentation of recursive functions is equation based. Also note Barendregt’s account of the lambda calculus is based on equational logic with distinct equalities, ≡, =α , =β . But presenting computation rules as equations is a bit misleading. ...
A counterexample to the infinite version of a
... Tan Chong Hui is a second year student at the National University of Singapore. He currently holds the post of Academic Head in the Mathematics Society of the National University of Singapore. He has represented Singapore in the International Mathematical Olympiad held in China and Sweden. ...
... Tan Chong Hui is a second year student at the National University of Singapore. He currently holds the post of Academic Head in the Mathematics Society of the National University of Singapore. He has represented Singapore in the International Mathematical Olympiad held in China and Sweden. ...