Commutative subalgebras of the Grassmann algebra
نویسنده
چکیده
The maximal dimension of a commutative subalgebra of the Grassmann algebra is determined. It is shown that for any commutative subalgebra there exists an equidimensional commutative subalgebra spanned by monomials. It follows that the maximal dimension of a commutative subalgebra can be expressed in terms of the maximal size of an intersecting system of subsets of odd size in a finite set. 2010 MSC: 15A75 (Primary); 05D05 (Secondary); 16W55 (Secondary); 13A02 (Secondary)
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