2 problems

Bruns–Gubeladze conjecture on graded algebra retracts of polytopal algebras
Let $k$ be a field, let $A$ be a polytopal algebra over $k$ , and let $B$ be a graded algebra retract of $A$ . Bruns–Gubeladze conjecture. $B$ is again a polytopal algebra over $k$ .…
openFrom papersalgebra-retracts polytopal-algebras stanley-reisner-rings
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6
The base conjecture for graded retracts of monomial quotients
Base conjecture. Every graded algebra retract of $S/I$ has a base.
openFrom papersalgebra-retracts graded-rings monomial-ideals
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5

Bruns–Gubeladze conjecture on graded algebra retracts of polytopal algebras