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Let $A=KQ/I$ be a quiver algebra such that the coefficients of the relations in the admissible ideal $I$ consist only of the field elements $0,1$ and $-1$.

Question 1: Is it true for every basic idempotent $e$ that the algebra $eAe$ is isomorphic to a quiver algebra such that the admissible ideal $I$ contains only the field elements $0,1$ and $-1$?

Question 2: Is it true in case $A$ is QF-3 and $e$ is such that $eA$ is the basis version of a minimal faithful projective-injective $A$-module?

Question 3: Can one check with QPA whether a given quiver algebra $A$ is isomorphic to a quiver algebra with relations containing only field elements $0,-1$ and 1?

(asked before on MSE: https://math.stackexchange.com/questions/3797390/field-elements-in-quiver-and-relations )

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    $\begingroup$ An ideal that contains the identity element is necessarily the whole algebra. So I don't think what you are asking for is possible (unless the quiver consists of at most one vertex, and the field has at most three elements). Perhaps I am missing the point of your question? $\endgroup$ Sep 3, 2020 at 19:14
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    $\begingroup$ @HughThomassupportsMonica Thanks, I mean that the coefficients of the relations only have field elements 1 or -1 allowed. I edit it. $\endgroup$
    – Mare
    Sep 3, 2020 at 19:24

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