Bifurcus semigroups and rings

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“…The following result generalizes (2)- (9) of [Adams et al 2009, Theorem 1.1] for k-furcus semigroups, and can be proved by straightforward modifications of the arguments in that paper.…”

“…In [Adams et al 2009], it is shown that several important families of semigroups are not bifurcus. Straightforward modifictions show that these same families of semigroups cannot be k-furcus for any k ≥ 2.…”

“…Vadim Ponomarenko and coworkers [Adams et al 2009] introduced and studied the notion of bifurcus semigroups, a class of semigroups with "bad" factorization properties: a semigroup S is bifurcus if every nonunit nonatom can be bifurcated, that is, expressed as the product of exactly two atoms in S. They gave examples, showed that certain important families of semigroups cannot be bifurcus, and calculated several factorization-theoretic invariants of bifurcus semigroups. Further examples of bifurcus semigroups can be found in [Baeth et al 2011].…”

“…We now give an analog to [Adams et al 2009, Theorem 1.1(1)] when S is strongly k-furcus. This analog was omitted from our Theorem 2.1 since the hypothesis of S being k-furcus but not strongly k-furcus seems not to be enough information to guarantee these results.…”

k-furcus semigroups

“…Vadim Ponomarenko and coworkers [Adams et al 2009] introduced and studied the notion of bifurcus semigroups, a class of semigroups with "bad" factorization properties: a semigroup S is bifurcus if every nonunit nonatom can be bifurcated, that is, expressed as the product of exactly two atoms in S. They gave examples, showed that certain important families of semigroups cannot be bifurcus, and calculated several factorization-theoretic invariants of bifurcus semigroups. Further examples of bifurcus semigroups can be found in .…”