# Revision history [back]

### Compute radical and primitive idempotents of a quotient algebra

Hi,

I tried the following:

R.$<$x,y$>$=PolynomialRing(QQ,2)

I=Ideal(x^2,y^2)

S=R.quotient(I)

I have the following question:

I woukd like to compute with SAGE the Jacobson radical of the algebra S and a block decomposition of S into indecomposable algebras (or compute the primitive idempotents).

Of course, you can compute this by hand, but I am interested in more complicated examples, too, but wanted to start with this simple example.

Since I am relatively new to SAGE, I unfortunately do not know how to compute this.

I would be grateful for any help.

### Compute radical and primitive central idempotents of a quotient algebra

Hi,

I tried the following:

R.$<$x,y$>$=PolynomialRing(QQ,2)

I=Ideal(x^2,y^2)

S=R.quotient(I)

I have the following question:

I woukd like to compute with SAGE the Jacobson radical of the algebra S and a block decomposition of S into indecomposable algebras (or compute the primitive central idempotents).

Of course, you can compute this by hand, but I am interested in more complicated examples, too, but wanted to start with this simple example.

Since I am relatively new to SAGE, I unfortunately do not know how to compute this.

I would be grateful for any help.

### Compute radical and central idempotents of a quotient algebra

Hi,

I tried the following:

R.$<$x,y$>$=PolynomialRing(QQ,2)

I=Ideal(x^2,y^2)

S=R.quotient(I)

I have the following question:

I woukd like to compute with SAGE the Jacobson radical of the algebra S and the central idempotents).

Of course, you can compute this by hand, but I am interested in more complicated examples, too, too (also in matrix algebras), but wanted to start with this simple example.

Since I am relatively new to SAGE, I unfortunately do not know how to compute this.

I would be grateful for any help.

### Compute radical and central idempotents of a quotient algebra

Hi,

I tried the following:

R.$<$x,y$>$=PolynomialRing(QQ,2)

I=Ideal(x^2,y^2)

S=R.quotient(I)

I have the following question:

I woukd like to compute with SAGE the Jacobson radical of the algebra S S, all primitive orthogonal idempotents and the central idempotents).

Of course, you can compute this by hand, but I am interested in more complicated examples, too (also in matrix algebras), but wanted to start with this simple example.

Since I am relatively new to SAGE, I unfortunately do not know how to compute this.

I would be grateful for any help.

### Compute radical and idempotents of a quotient algebra

Hi,

I tried the following:

R.$<$x,y$>$=PolynomialRing(QQ,2)

I=Ideal(x^2,y^2)

S=R.quotient(I)

I have the following question:

I woukd like to compute with SAGE the Jacobson radical of the algebra S, all primitive orthogonal idempotents and the central idempotents).idempotents.

Of course, you can compute this by hand, but I am interested in more complicated examples, too (also in matrix algebras), but wanted to start with this simple example.

Since I am relatively new to SAGE, I unfortunately do not know how to compute this.

I would be grateful for any help.

 6 No.6 Revision slelievre 12586 ●11 ●122 ●250 http://carva.org/samue...

### Compute radical and idempotents of a quotient algebra

Hi,

I tried the following:

R.$<$x,y$>$=PolynomialRing(QQ,2)

I=Ideal(x^2,y^2)

S=R.quotient(I)

R.<x,y>=PolynomialRing(QQ,2)
I=Ideal(x^2,y^2)
S=R.quotient(I)


I have the following question:

I woukd would like to compute with SAGE the Jacobson radical of the algebra S, all primitive orthogonal idempotents and the central idempotents.

Of course, you can compute this by hand, but I am interested in more complicated examples, too (also in matrix algebras), but wanted to start with this simple example.

Since I am relatively new to SAGE, Sage, I unfortunately do not know how to compute this.

I would be grateful for any help.

 7 None slelievre 12586 ●11 ●122 ●250 http://carva.org/samue...

### Compute radical and idempotents of a quotient algebra

I tried the following:

R.<x,y>=PolynomialRing(QQ,2)
I=Ideal(x^2,y^2)
S=R.quotient(I)
R.<x, y> = PolynomialRing(QQ, 2)
I = Ideal(x^2, y^2)
S = R.quotient(I)


I have the following question:

I would like to compute with SAGE Sage the Jacobson radical of the algebra S, S, all primitive orthogonal idempotents and the central idempotents.

Of course, you can compute this by hand, but I am interested in more more complicated examples, too (also in matrix algebras), but wanted to to start with this simple example.

Since I am relatively new to Sage, I unfortunately do not know how to compute this.

I would be grateful for any help.