# Questions tagged [universal-algebra]

The study of algebraic structures and properties applying to large classes of such structures. For example, ideas from group theory and ring theory are extended and considered for structures with other signatures (systems of basic or fundamental operations).

**58**

**5**answers

### Does "finitely presented" mean "always finitely presented"? (Answered: Yes!)

**39**

**1**answer

### Identities of commutators

**35**

**19**answers

### Counterexamples in universal algebra

**35**

**6**answers

### Do convolution and multiplication satisfy any nontrivial algebraic identities?

**34**

**21**answers

### Why are so few operations with arity bigger than 2?

**32**

**7**answers

### Do non-associative objects have a natural notion of representation?

**28**

**4**answers

### How dangerous are set-size assumptions?

**27**

**3**answers

### Lawvere theories versus classical universal algebra

**25**

**1**answer

### A preprint of Sela concerning the work of Kharlampovich-Miyasnikov

**22**

**1**answer

### Are there axioms satisfied in commutative rings and distributive lattices but not satisfied in commutative semirings?

**22**

**0**answers

### Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?

**21**

**4**answers

### Varieties where every algebra is free

**20**

**3**answers

### Relation between monads, operads and algebraic theories

**20**

**1**answer

### Does sine interact equationally with addition alone?

**19**

**3**answers

### Why are ring actions much harder to find than group actions?

**19**

**2**answers

### Do all subtraction-free identities tropicalize?

**19**

**2**answers

### Why does abelianization preserve finite products, really?

**18**

**4**answers

### Complete Boolean algebra not isomorphic to a $\sigma$-algebra

**18**

**4**answers

### Representation theorem for modular lattices?

**18**

**2**answers

### Constructive proof of existence of free algebras for infinitary equational theories

**17**

**2**answers

### Relation between monads, operads and algebraic theories (Again)

**17**

**2**answers

### Why is every variety of bands determined by a single identity?

**17**

**1**answer

### What are the relations between conjugates and commutators?

**17**

**1**answer

### Topological universal algebra: what is a variety?

**17**

**0**answers

### Why did Bourbaki not use universal algebra?

**16**

**3**answers

### What is the theory of polynomials?

**16**

**1**answer

### So, did Poincaré prove PBW or not?

**16**

**1**answer

### Does every commutative variety of algebras have a cogenerator?

**15**

**3**answers

### Is the Amitsur-Levitzki identity essentially unique?

**15**

**1**answer

### What is a module over a Boolean ring?

**15**

**2**answers

### Formally undecidable problems on finitely presented quandles

**14**

**4**answers

### Are norms intrinsically $\mathbb{R}$-valued?

**14**

**2**answers

### Contexts and notations for composing asymmetric simplices

**13**

**2**answers

### Free division rings?

**13**

**3**answers

### $fgf = f$, $gfg = g$, $fg$ not necessarily identity, what is this called?

**13**

**4**answers

### The groupoid of algebraic expressions and proofs

**13**

**1**answer

### characterization of subalgebras of universal enveloping algebra coming from Lie subalgebras

**13**

**1**answer

### Which categories are the categories of models of a Lawvere theory?

**13**

**2**answers

### What is the status of (universal) algebra in type theory?

**13**

**3**answers

### About a construction of Borel $\sigma$-algebra associated to a lattice

**13**

**0**answers

### The free complete lattice on three generators, beyond ZF

**13**

**0**answers

### Is there a finite equational basis for the join of the commutative and associative equations?

**12**

**5**answers

### Jonsson Boolean algebras?

**12**

**0**answers

### Birkhoff's HSP theorem in categories other than $\mathbf{Set}$

**11**

**3**answers

### Comparing the existing formulations of universal algebra and their levels of generality

**11**

**2**answers

### What is known about ideal and divisibility lattices of GCD domains and their generalizations?

**11**

**3**answers

### IBN for algebraic theories

**11**

**5**answers

### What are the invariant Pseudo-differential operators on a Lie group?

**11**

**2**answers

### Uses of Zorn's Lemma when the thing is actually unique

**11**

**0**answers