Question

Given: A set R with two operations + and * is a ring if the following eight properties are shown to be true: • Closure property of addition: for all s and t in R, s + t is also in R • Closure property of multiplication: for all s and t in R, s * t is also in R • Additive identity property: there exists an element 0 in R such that s + 0 = s for all s in R • Additive inverse property: for every s in R, there exists t in R, such that s + t = 0 • Associative property of addition: for every q, s, and t in R, q + (s + t) = (q + s) + t • Associative property of multiplication: for every q, s, and t in R, q x (s x t) = (q x s) x t • Commutative property of addition: for all s and t in R, s + t = t + s • Left distributive property of multiplication over addition: for every q, s, and t in R, q * (s + t) = q * s + q * t • Right distributive property of multiplication over addition: for every q, s, and t in R, (s + t) * q = s * q + t * q Consider the set M(2?) of 2 × 2 matrices with even integer entries. The notation 2? denotes the

          Given:

A set R with two operations + and * is a ring if the following eight properties are shown to be true:
• Closure property of addition: for all s and t in R, s + t is also in R
• Closure property of multiplication: for all s and t in R, s * t is also in R
• Additive identity property: there exists an element 0 in R such that s + 0 = s for all s in R
• Additive inverse property: for every s in R, there exists t in R, such that s + t = 0
• Associative property of addition: for every q, s, and t in R, q + (s + t) = (q + s) + t
• Associative property of multiplication: for every q, s, and t in R, q x (s x t) = (q x s) x t
• Commutative property of addition: for all s and t in R, s + t = t + s
• Left distributive property of multiplication over addition: for every q, s, and t in R, q * (s + t) = q * s + q * t
• Right distributive property of multiplication over addition: for every q, s, and t in R, (s + t) * q = s * q + t * q

Consider the set M(2?) of 2 × 2 matrices with even integer entries. The notation 2? denotes the

Given:

A set R with two operations + and * is a ring if the following eight properties are shown to be true:
• Closure property of addition: for all s and t in R, s + t is also in R
• Closure property of multiplication: for all s and t in R, s * t is also in R
• Additive identity property: there exists an element 0 in R such that s + 0 = s for all s in R
• Additive inverse property: for every s in R, there exists t in R, such that s + t = 0
• Associative property of addition: for every q, s, and t in R, q + (s + t) = (q + s) + t
• Associative property of multiplication: for every q, s, and t in R, q x (s x t) = (q x s) x t
• Commutative property of addition: for all s and t in R, s + t = t + s
• Left distributive property of multiplication over addition: for every q, s, and t in R, q * (s + t) = q * s + q * t
• Right distributive property of multiplication over addition: for every q, s, and t in R, (s + t) * q = s * q + t * q

Consider the set M(2?) of 2 × 2 matrices with even integer entries. The notation 2? denotes the

Added by Randy T.

Question

Please give Ace some feedback