Graph-monoids are introduced as algebraic objects which correspond to congruences over graphs. Varieties are defined, and a one-to-one correspondence between varieties of graph-monoids and varieties of graph-congruences is demonstrated. This is viewed as a generalization of the known correspondence between monoid varieties and congruence varieties. Some classification and effective characterizations of graph-monoid varieties are obtained. These are used to decide membership in the wreath product of certain monoids varieties and the variety of definite semigroups.

Given a finite set X of states, a finite set of transformations of X (generators), and another transformation f of X, we analyze the complexity of the membership problem, which consists in deciding whether f can be obtained by composition of the generators. This problem is studied for various classes (pseudovarieties) of monoids. It is shown that the complexity is NP-hard for monoids of threshold 2 or more, and NP-complete in commutative, J- and R-trivial monoids. For idempotent monoids (aperiodic of threshold one), the problem is NP-complete in the general case; subcases are analyzed, and a largest class of aperiodic monoids is identified for which the problem is in FL, as well as a largest class for which the problem is not NP-hard. / The problem which consists in characterizing an idempotent monoid is also addressed: given a set of transformations, it can be decided in NC$ sp2$ whether the monoid they generate is idempotent. Similar tests are given for three subclasses of idempotent monoids: R$ sb1$, L$ sb1$, and N$ sb3$; in all three cases, the complexity is NC$ sp1$. / A sequential upper bound is also given for each of the parallel complexities given above.

No description available.

No description available.

<p> This thesis makes a small study of various kinds of submonoids of abelian monoids, of the lattice of submonoids of an abelian monoid, and of the concept of unique factorization in abelian monoids. Also, the main concepts in category theory are examined in the special case of the category of abelian monoids and some of its subcategories. </p> / Thesis / Master of Science (MSc)

No description available.

No description available.

No description available.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2006. / Title from title screen (site viewed on Sep. 12, 2006). PDF text of dissertation: 109 p. : ill. ; 0.71Mb. UMI publication number: AAT 3208081. Includes bibliographical references. Also available in microfilm, microfiche and paper format.

No description available.