We consider an algebra of entire functions of exponential type that are bounded on the real line. It is called Bernstein algebra. The criterion for a function to be a divisor of this algebra is obtained. We formulate the criterion in terms of so-called “slow decrease”. For the Schwartz algebra and Beurling-Bjorck algebra similar criteria are known. We also investigate the connections between the set of divisors of the Bernstein algebra and class of sine-type functions
