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The Specht module of the partition λ is the module generated by the elements ET as T runs through all tableaux of shape λ. The Specht module has a basis of elements ET for T a standard Young tableau . A gentle introduction to the construction of the Specht module may be found in Section 1 of "Specht Polytopes and Specht Matroids".
However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school (grades 9 to 12, for students typically aged 14 to 18), while seventeen states and the District of Columbia require four. [2]
Example: a graded vector space is an example of a graded module over a field (with the field having trivial grading). Example: a graded ring is a graded module over itself. An ideal in a graded ring is homogeneous if and only if it is a graded submodule. The annihilator of a graded module is a homogeneous ideal.
Length of a module. In algebra, the length of a module over a ring is a generalization of the dimension of a vector space which measures its size. [ 1] page 153 It is defined to be the length of the longest chain of submodules. For vector spaces (modules over a field), the length equals the dimension. If is an algebra over a field , the length ...
Module (mathematics) In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module also generalizes the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers . Like a vector space, a module is an additive abelian ...
mathcounts .org. Mathcounts, stylized as MATHCOUNTS, is a non-profit organization that provides grades 6-8 extracurricular mathematics programs in all U.S. states, plus the District of Columbia, Puerto Rico, Guam and U.S. Virgin Islands. Its mission is to provide engaging math programs for middle school students of all ability levels to build ...
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This quarter system was adopted by the oldest universities in the English-speaking world (Oxford, founded circa 1096, [1] and Cambridge, founded circa 1209 [2]). Over time, Cambridge dropped Trinity Term and renamed Hilary Term to Lent Term, and Oxford also dropped the original Trinity Term and renamed Easter Term as Trinity Term, thus establishing the three-term academic "quarter" year widely ...