1. The non-zero elements of a finite field form a cyclic group under multiplication. 2. Only sequences with a finite number of non-zero elements are in " Y ". 3. A non-zero element of the field group under multiplication. 4. A non-zero element in H does double transpositions within 4 or 6 of the columns. 5. Zero may be the square of some non-zero elements . 6. Chien search improves upon the above by selecting a specific order for the non-zero elements . 7. Quaternions form a division algebra every non-zero element has an inverse whereas Pauli matrices do not. 8. After every non-zero element the additional zeroes can be implied and do not need to be stored. 9. In mathematics, a "'zero element "'is one of several generalizations of the number zero to other algebraic structures. 10. As an affine space does not have a zero element , an affine homomorphism does not have a kernel.
