algebra_fan
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 18 How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset$ look like? 10 Can a Gaussian integer matrix have an inverse with Gaussian integer entries? 10 Product of two ideals doesn't equal the intersection 8 If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field. 6 Is this $\left|\left(\frac{a}{b}\right)^n-\left(\frac{a}{b}\right)^{n-1}\right|$ bounded?

### Reputation (1,556)

 +5 the localization of a ring is an integral domain iff the annihilators of zero divisors are comaximal ideals +10 Difference between bijection and isomorphism? +10 How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset$ look like? +10 If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.

### Questions (3)

 26 A finite ring is a field if its units $\cup\ \{0\}$ comprise a field of characteristic $\ne 2$ 10 the localization of a ring is an integral domain iff the annihilators of zero divisors are comaximal ideals 2 Justification for applying Rouché's theorem for an unbounded domain

### Tags (32)

 30 linear-algebra × 5 16 matrices × 2 29 elementary-set-theory × 4 12 field-theory × 4 22 ring-theory × 4 8 fake-proofs × 2 19 abstract-algebra × 7 8 commutative-algebra 17 complex-numbers × 3 8 modules

### Account (1)

 Mathematics 1,556 rep 1912