Questions about properties of rings, integral domains, or fields, including proving a structure is a field, an integral domain, or determining field isomorphisms and existence of fields of given order.
A subset $W$ of the set of real numbers is called a ring if it contains 1 and if for all $a, b \in W$, the numbers $a - b$ and $ab$ are also in $W$. Let $S = \left\{ \left. \frac{m}{2^n} \right\rvert\, m, n \text{ integers} \right\}$ and $T = \left\{ \left. \frac{p}{q} \right\rvert\, p, q \text{ integers}, q \text{ odd} \right\}$. Then (A) neither $S$ nor $T$ is a ring (B) $S$ is a ring, $T$ is not a ring (C) $T$ is a ring, $S$ is not a ring (D) both $S$ and $T$ are rings
A subset $W$ of the set of real numbers is called a ring if it contains 1 and if for all $a , b \in W$, the numbers $a - b$ and $a b$ are also in $W$. Let $S = \left\{ \left. \frac { m } { 2 ^ { n } } \right\rvert\, m , n \text{ integers} \right\}$ and $T = \left\{ \left. \frac { p } { q } \right\rvert\, p , q \text{ integers}, q \text{ odd} \right\}$. Then: (a) neither $S$ nor $T$ is a ring (b) $S$ is a ring, $T$ is not a ring. (c) $T$ is a ring, $S$ is not a ring. (d) both $S$ and $T$ are rings.
A subset $W$ of the set of real numbers is called a ring if it contains 1 and if for all $a , b \in W$, the numbers $a - b$ and $a b$ are also in $W$. Let $S = \left\{ \left. \frac { m } { 2 ^ { n } } \right\rvert\, m , n \text{ integers} \right\}$ and $T = \left\{ \left. \frac { p } { q } \right\rvert\, p , q \text{ integers}, q \text{ odd} \right\}$. Then: (a) neither $S$ nor $T$ is a ring (b) $S$ is a ring, $T$ is not a ring. (c) $T$ is a ring, $S$ is not a ring. (d) both $S$ and $T$ are rings.
A subset $W$ of the set of real numbers is called a ring if it contains 1 and if for all $a, b \in W$, the numbers $a - b$ and $ab$ are also in $W$. Let $S = \left\{ \left. \frac{m}{2^n} \right\rvert\, m, n \text{ integers} \right\}$ and $T = \left\{ \left. \frac{p}{q} \right\rvert\, p, q \text{ integers}, q \text{ odd} \right\}$. Then (A) neither $S$ nor $T$ is a ring (B) $S$ is a ring, $T$ is not a ring (C) $T$ is a ring, $S$ is not a ring (D) both $S$ and $T$ are rings
A subset $W$ of the set of real numbers is called a ring if it contains 1 and if for all $a , b \in W$, the numbers $a - b$ and $a b$ are also in $W$. Let $S = \left\{ \left. \frac { m } { 2 ^ { n } } \right\rvert\, m , n \text{ integers} \right\}$ and $T = \left\{ \left. \frac { p } { q } \right\rvert\, p , q \text{ integers}, q \text{ odd} \right\}$. Then (A) neither $S$ nor $T$ is a ring (B) $S$ is a ring, $T$ is not a ring (C) $T$ is a ring, $S$ is not a ring (D) both $S$ and $T$ are rings