Ring detail


Name: Nielsen's semicommutative ring that isn't McCoy

Description: Let $A=F_2\langle a_0,a_1,a_2,a_3, b_0,b_1\rangle$ be a free algebra over the field of two elements and with noncommuting indeterminates. Let $I$ be the ideal generated by the following elements: $a_0b_0$, $a_1b_0+a_0b_1$, $a_1b_1+a_2b_0$, $a_2b_1+a_3b_0$, $a_3b_1$, $a_0a_j (0\leq j\leq 3)$, $a_3a_j (0\leq j\leq 3)$, $a_1a_j+a_2a_j (0\leq j\leq 3)$, $b_ib_j(0\leq i,j,\leq 1)$, $b_ia_j(0\leq i\leq 1, 0\leq j\leq 3)$. The ring is the quotient of $A$ by these generators.

Keywords free algebra quotient ring

Reference(s):

  • P. P. Nielsen. Semi-commutativity and the {M}c{C}oy condition. (2006) @ Section 3 p 138



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  • = does not have the property
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