body in nLab

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In superalgebra

In the context of superalgebra, the quotient of a superalgebra by the ideal generated by its odd part (its “soul”) is called its body.

See at superalgebra – Adjoints to inclusion of plain algebras and at bosonic modality.

This terminology is (for the special case of Grassmann algebras at least) due to DeWitt 92, p. 1

References

• Bryce DeWitt, Supermanifolds, Monographs on Mathematical Physics, Cambridge University Press (1984) [doi:10.1017/CBO9780511564000]