#### Hall 123

#### Completability of Unimodular Rows

#### Krishanu Dan

##### IMSc

*Let A be commutative ring with unity. An element [a_1, a_2, ... , a_n] in A^n is called unimodular (of length n) if the ideal generated by a_1, a_2, ... , a_n is the whole ring A. We say a unimodular row [a_1, a_2, ... , a_n] is completable if there is an nxn invertible matrix M, with entries from A, whose first row is [a_1 a_2 ... a_n]. We will give some criterion for a unimodular row to be completable, which depends on the ring and also on the length.*

Done