1.6.33 Fields, Groups, Rings

Condition: Having checked the axioms, to establish whether the specified algebra is with two binary operations by a half -ring, a ring. At the same time: a) for a half -ring (not a ring), to check whether the semi -ring is a switching, hypothetic, closed; b) For the ring, check whether it will be Boolev, whether there are zero dividers in it, whether the ring is a field. A set algebra: a lot of matrices of the species \ (\ left (\ begin {array} {ll} ah \\ 0 & b \ end {array} \ right) \), where \ (a, b \ in {0.1 \} \) with operations of addition and multiplication operations matrices, and the operations of addition and multiplication of elements are performed in the half -ring \ (\ mathbb {b} \).