# Questions tagged [ra.rings-and-algebras]

Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.

**39**

**6**answers

### An algebra of "integrals"

**80**

**5**answers

### When is $A$ isomorphic to $A^3$?

**25**

**2**answers

### Codimension of the range of certain linear operators

**89**

**2**answers

### $A$ is isomorphic to $A \oplus \mathbb{Z}^2$, but not to $A \oplus \mathbb{Z}$

**59**

**3**answers

### What is the current status of the Kaplansky zero-divisor conjecture for group rings?

**23**

**6**answers

### prime ideals in C([0,1])

**33**

**1**answer

### Whence “homomorphism” and “homomorphic”?

**5**

**1**answer

### Terminology for a monoid $H$ s.t. $xy \in H^\times$ only if $x, y \in H^\times$

**92**

**11**answers

### Can a non-surjective polynomial map from an infinite field to itself miss only finitely many points?

**15**

**1**answer

### Are there non-reflexive modules isomorphic to their bi-dual?

**14**

**1**answer

### Finite dimensional real division algebras

**6**

**1**answer

### Is there an integral fusion ring which is not of Frobenius type?

**2**

**1**answer

### Terminology for a monoid $(H, \cdot)$ s.t. $ax=a$ or $xa =a$ only if $x$ is a unit

**105**

**18**answers

### How do you decide whether a question in abstract algebra is worth studying?

**31**

**2**answers

### Dimension of infinite product of vector spaces

**39**

**5**answers

### When does a ring surjection imply a surjection of the group of units?

**23**

**7**answers

### Commutative subalgebras of M_n

**13**

**5**answers

### reduced ⊗ reduced = reduced; what about connected?

**31**

**6**answers

### Bass' stable range of $\mathbf Z[X]$

**17**

**3**answers

### Finite non-commutative ring with few invertible (unit) elements

**28**

**1**answer

### Does GL_n(Z) have a noetherian group ring?

**10**

**3**answers

### About the classification of commutative and of cocommutative, fin. dim. Hopf algebras

**16**

**3**answers

### Characterising categories of vector spaces

**6**

**1**answer

### Solid rings and Tor

**11**

**1**answer

### Does this algebra have finite global dimension ? (Human vs computer)

**4**

**0**answers

### Rewrite sum of radicals equation as polynomial equation

**2**

**1**answer

### Are there infinitely many L-rigs?

**0**

**2**answers

### Rank of a $ \mathbb{Z}_{p}[[T]] $ module

**107**

**2**answers

### How would you solve this tantalizing Halmos problem?

**62**

**25**answers

### Linear Algebra Texts?

**25**

**8**answers

### What is the "right" definition of a ring?

**45**

**9**answers

### What are the reasons for considering rings without identity?

**48**

**7**answers

### Good lattice theory books?

**74**

**1**answer

### $R$ is isomorphic to $R[X,Y]$, but not to $R[X]$

**19**

**4**answers

### Relationship between the cohomology of a group and the cohomology of its associated Lie algebra

**12**

**1**answer

### What are tame and wild hereditary algebras?

**15**

**3**answers

### Which is the correct universal enveloping algebra in positive characteristic?

**29**

**1**answer

### Are Conway's omnific integers the Grothendieck group of the ordinals under commutative addition?

**17**

**6**answers

### What's an example of a transcendental power series?

**12**

**1**answer

### Explicit Bijection between Central Simple Algebras and twists of $\mathbb P^n$

**22**

**4**answers

### The number of ideals in a ring

**19**

**4**answers

### What is the geometric object corresponding to a subalgebra in a polynomial ring

**15**

**3**answers

### Existence of a ring with specified residue fields

**15**

**2**answers

### Which commutative groups are the group of units of some field?

**10**

**1**answer

### How many Lie and associative algebras over a finite field are there?

**7**

**2**answers

### *-homomorphisms between matrix algebras

**21**

**3**answers

### Can a module be an extension in two really different ways?

**17**

**3**answers

### Existence of translation-invariant basis on $C_c(\mathbb R)$

**14**

**1**answer

### Is the class of additive groups of rings axiomatizable?

**12**

**3**answers