Some results concerning uniformly (1-absorbing) primary ideals

Let [Formula: see text] be a commutative ring with [Formula: see text]. A proper ideal [Formula: see text] of [Formula: see text] is said to be a uniformly 1-absorbing primary if there exits a fixed [Formula: see text] and whenever [Formula: see text] for some nonunits [Formula: see text] then [Formula: see text] or [Formula: see text]. In addition to give various properties of uniformly 1-absorbing primary ideals, we characterize some important classes of rings such as von Neumann regular rings, UN-rings, nonlocal rings, fields and divided rings in terms of uniformly 1-absorbing primary ideals. Also, we investigate uniformly primary ideals and uniformly 1-absorbing primary ideals of amalgamated algebras [Formula: see text].