IRA accounts are not deductible or nondeductible, it's IRA contributions that are either deductible or nondeductible.
Covered by a retirement plan at work means that additions are made on behalf of the employee for the company's retirement plan tax year ending with or within the tax year of the employee. The employer indicates coverage by marking box 13 Retirement plan on the employee's W-2.
With sufficient compensation, anyone can make a traditional IRA contribution as long as they have not reached the year in which they reach age 70½. The only question is whether or not the contribution is deductible, determined by a combination of modified AGI, the individual's workplace retirement coverage and the individual's spouse's workplace retirement coverage.
