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### Semi-commutations and Partial commutations

M. Clerbout, Y. Roos, I. Ryl
2000 RAIRO - Theoretical Informatics and Applications
PARTIAL COMMUTATIONS AND SEMI-COMMUTATIONS Let us recall some définitions and some results about partial commutations and semi-commutations (for more details see [7] ). 0 = (E x E)\0.  ...  Let 0 be a semi-commutation (or a partial commutation) defined over an alphabet E and u be a word of E*.  ...

### Semi-commutations and Petri nets

Dang Van Hung, Elöd Knuth
1989 Theoretical Computer Science
A semkommutation is a generalization of a partial commutation. So-called traces are generated by partial commutations.  ...  A semi-commutation system S = (X, P) is a semr-Thue system, where X is a finite alphabet and P is a set of rules of the form ab + ba with Q, b E X and Q # b.  ...  Nivat for his helpful advice and criticism that led to significant improvements in the paper. We are also grateful to the referees for their reading the paper, and their criticism.  ...

### Semi-trace morphisms and rational transductions [chapter]

Pierre-André Wacrenier
1995 Lecture Notes in Computer Science
We investigate trace and semi-trace morphisms from an algebraic point of view thanks to rational transductions.  ...  The main result is a characterization of (semi-) trace morphisms which are equivalent to some rational transduction. Within this result we easily characterize context-free trace morphisms.  ...  Acknowledgments: I thanks the referees and Les Chtimis for their comments and remarks.  ...

### Semi-commutations

M. Clerbout, M. Latteux
1987 Information and Computation
We extend the notion of partial commutation by introducing that of semi-commutation which is its non-symetrical version.  ...  Let S= (X, P> be a semi-commutation system and w be a word of X*.  ...  sufficient condition concerning a semi-commutation,f'and a finite set F which ensures thatf(F*) is a regular language.  ...

### Page 3935 of Mathematical Reviews Vol. , Issue 93g [page]

1993 Mathematical Reviews
Whereas a partial commutation relation is symmetric, a semi-commutation corresponds to a rewriting sys- tem with rules of the form ab — ba.  ...  This paper surveys a number of results and open problems concerning semi-commutations. Af- ter the presentation of some basic lemmas, decomposition and composition of semi-commutations are discussed.  ...

### Page 1024 of Mathematical Reviews Vol. 35, Issue 5 [page]

1968 Mathematical Reviews
The authors characterize the subdirect products of a semi- group S and a rectangular band B and study the iso- morphy problem for these subdirect products in the case of a commutative reductive semigroup  ...  A. 5531 Two remarks on isomorphisms of commutative semi- groups. (Russian. English s ) Algebra i Logika Sem. 6 (1967), no. 1, 95-110.  ...

### Related representation theorems for rings, semi-rings, near-rings and semi-near-rings by partial transformations and partial endomorphisms

Hanns Joachim Weinert
1977 Proceedings of the Edinburgh Mathematical Society
In order to generalise these theorems to groups and rings whose addition may not be commutative, one has to deal with partial endomorphisms.  ...  Theorem 4a . 4a The set E = E(G, U, W, +) of all partial endomorphisms of groups (G, U, W,+) with commutative (W, +) is a ring (E, +,•), whose addition is commutative if the group (U,+) is commutative.  ...  Both last rows show that E is not closed with respect to addition, and for instance the element <p2+ (f>i= r of the semi-near-ring ({E),+,-)* is not  ...

### On the synchronization of semi-traces [chapter]

Klaus Reinhardt
1995 Lecture Notes in Computer Science
In this paper we give criteria, which tell us for given semi-traces in given semicommutation systems, whether they are synchronizable and whether the synchronization is again a semi-trace; and criteria  ...  , which tell us for given semi-commutation systems, whether all semi-traces have this property.  ...  Acknowledgment: I thank Volker Diekert, Klaus-Jörn Lange and an anonymous referee for helpful remarks.  ...

### On semi-star-related matrices

Jürgen Groβ
1997 Linear Algebra and its Applications
In this note we introduce semi-star-related matriees, investigate some of their properties, and demonstrate how the usual definition of Drazin's (1978) star partial ordering can be relaxed. © 1997 Elsevier  ...  Since semi-star-related matrices also star-commute, and the star partial ordering implies the semi-star relation (see Corollary 2), we easily obtain . rs A~.B ~ A..<B andA~lB.  ...  We say that A and B are semi-star-L L AB*. related, and we write A ~ B, if A*A ~< A* B and AA* ~< Note that semi-star-related matrices are a subclass of star-commuting matrices.  ...

### Reliable generalized and context dependent commutation relations [chapter]

Isabelle Biermann, Brigitte Rozoy
1997 Lecture Notes in Computer Science
We give necessary conditions and sufficient conditions for such relations to be reliable (preserve recognizability) and we provide a semi-algorithm to compute the closure of a language.  ...  Trace theory was introduced to capture the behavior of 1safe Petri nets, it is based on partial commutation relations where two adjacent letters are allowed to permute.  ...  -partial commutations where R is a semi-commutation relation and R is a generalized commutation relation.  ...

### Page 977 of Mathematical Reviews Vol. 33, Issue 5 [page]

1967 Mathematical Reviews
The main purpose of the paper is to find necessary and sufficient conditions on a commutative idempotent semi- group A for there to exist a non-commutative semigroup B such that A and B are lattice isomorphic  ...  A commutative semi- group has finite d-width if and only if it is a finite band of semigroups each of which is an ideal extension of a group of finite d-width by a finite nilpotent semigroup and at most  ...

### Multiendomorphisms of hypergroupoids

G. Gentile
2006 International Mathematical Forum
We show that, if (H, * ) is a commutative semi-hypergroup, these multiendomorphisms form a G-semiring (E, +, •, ≤), where the operation + is induced by * , • is the usual composition of maps • and ≤ is  ...  We introduce the notion of multiendomorphism in a hypergroupoid and the notion of G-semiring.  ...  End-closed and End g -closed semi-hypergroups In general, if (H, * ) is a commutative semi-hypergroup, the structure (E(H), +, •) is not a semiring, since in general the distributive law does not holds  ...

### Page 237 of American Journal of Mathematics Vol. 74, Issue 1 [page]

1952 American Journal of Mathematics
(An operator P is semi-normal if P*P and PP* are comparable with respect to the usual partial ordering of Hermitian operators.)  ...  normal, or even semi-normal.  ...

### Page 283 of Mathematical Reviews Vol. 35, Issue 2 [page]

1968 Mathematical Reviews
Necessary and sufficient conditions are given for a binary relation to semi-commute with a set of partial transformations of A.  ...  A binary relation p is called semi-commuting with a set of binary relations X if pairs (x, p) are semi-commutative for all y ¢ X.  ...

### Semigroups of quasinormal operators

Mary Embry
1982 Pacific Journal of Mathematics
and a strongly continuous self-adjoint semi-group {h(t)} on ^ such that {Q t } is unitarily equivalent to {N t }®{h(t)L t } on ^®^{3T) 9 where {LJ is the forward translation semi-group on £f 2 (^f) and  ...  Strongly continuous semi-groups {Q t } of quasinormal operators on Hubert space are characterized as follows: there exist Hubert spaces Sf and -%% a strongly continuous normal semi-group {N t } on Ό?  ...  This follows from Theorem 2(ii) and the fact that a quasinormal operator is normal if and only if the partial isometry in the polar decomposition of Q is normal.  ...
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