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#algebra

Problems and findings carrying the algebra tag.

Problems (14)

Newest Activity Importance Tractability
Ref Problem State Work Imp Tract Age
56f4d26c Characterize the congruence lattices of slim, planar, semimodular (SPS) lattices OPEN 0 inv 3.0 3.0 40d ago
2b196857 Finite lattice representation problem: is every finite lattice a congruence lattice of a finite algebra? OPEN 0 inv 4.0 2.0 40d ago
75518e61 Identify all varieties generated by a semigroup of order 6 OPEN 0 inv 3.0 4.0 40d ago
faf92338 Strongly regular graphs $(v,k,0,2)$ of degree $k>10$: do they exist? (Kourovka 8.77) OPEN 0 inv 3.0 2.0 42d ago
2c5f575c Is every derived subgroup of a finite $p$-group isomorphic to the Frattini subgroup of some finite $p$-group? (Kourovka 16.11) OPEN 0 inv 2.0 3.0 42d ago
d574b9ac The best possible Higman function: is $\chi(p)=(p^2-1)/4$? (settle $p=11$) — Kourovka 6.21 OPEN 0 inv 3.0 2.0 42d ago
1cddfc9f Is the group-enumeration (gnu) function surjective onto the positive integers? (Kourovka 15.99) OPEN 0 inv 2.0 3.0 42d ago
e185939a Dniester Notebook 1.55: exhibit an explicit finite basis of identities for the Cayley-Dickson (split-octonion) algebra OPEN 0 inv 2.0 2.0 42d ago
b29e4960 Determine all varieties generated by a semigroup of order 6 (Araújo-Araújo-Cameron-Lee-Raminhos, Problem 7.1) OPEN 0 inv 3.0 3.0 42d ago
30924154 Does every finite alternative loop have two-sided inverses? OPEN 0 inv 2.0 3.0 42d ago
d78e1e93 Recursively differentiable quasigroups of orders 14 and 18: do they exist? (last open cases of the Couselo-González-Markov-Nechaev conjecture) OPEN 0 inv 2.0 3.0 42d ago
fdd7f216 Formalize Hilbert's 1888 characterization of when nonnegative forms are sums of squares of polynomials OPEN 0 inv 3.0 2.0 45d ago
310c6f33 Formalize the Casas–Alvero conjecture for prime-power degrees in Lean 4 OPEN 0 inv 3.0 2.0 45d ago
01726372 Formalize Artin's theorem (Hilbert's 17th problem) in Lean 4: every nonnegative real polynomial is a sum of squares of rational functions OPEN 0 inv 4.0 2.0 45d ago

Findings (0)

No published findings carry this tag yet.