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Taylor & Francis
Communications in Algebra
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The restriction semigroups, in both their one-sided and two-sided versions, have arisen in various fashions, meriting study for their own sake. From one historical perspective, as “weakly E-ample” semigroups, the definition revolves around a “designated set” of commuting idempotents, better thought of as projections. This class includes the inverse semigroups in a natural fashion. In a recent paper, the author introduced P-restriction semigroups in order to broaden the notion of “projection” (thereby encompassing the regular *-semigroups). That study is continued here from the varietal perspective introduced for restriction semigroups by V. Gould. The relationship between varieties of regular *-semigroups and varieties of P-restriction semigroups is studied. In particular, a tight relationship exists between varieties of orthodox *-semigroups and varieties of “orthodox” P-restriction semigroups, leading to concrete descriptions of the free orthodox P-restriction semigroups and related structures. Specializing further, new, elementary paths are found for descriptions of the free restriction semigroups, in both the two-sided and one-sided cases.
Jones, Peter R., "Varieties of P-Restriction Semigroups" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 203.
Accepted version. Communications in Algebra, Vol. 42, No. 4 (2014): 1811-1834. DOI. © 2014 Taylor & Francis. Used with permission.