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Near heaps

Ian Hawthorn, Tim Stokes (2011)

Commentationes Mathematicae Universitatis Carolinae

On any involuted semigroup ( S , · , ' ) , define the ternary operation [ a b c ] : = a · b ' · c for all a , b , c ∈ S . The resulting ternary algebra ( S , [ ] ) satisfies the para-associativity law [ [ a b c ] d e ] = [ a [ d c b ] e ] = [ a b [ c d e ] ] , which defines the variety of semiheaps. Important subvarieties include generalised heaps, which arise from inverse semigroups, and heaps, which arise from groups. We consider the intermediate variety of near heaps, defined by the additional laws [ a a a ] = a and [ a a b ] = [ b a a ] . Every Clifford semigroup is a near heap when viewed as a semiheap, and we show that the Clifford semigroup...

Nil-extensions of completely simple semirings

Sunil K. Maity, Rituparna Ghosh (2013)

Discussiones Mathematicae - General Algebra and Applications

A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.

Non-looping string rewriting

Alfons Geser, Hans Zantema (1999)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Non-Looping String Rewriting

Alfons Geser, Hans Zantema (2010)

RAIRO - Theoretical Informatics and Applications

String rewriting reductions of the form t → R + u t v , called loops, are the most frequent cause of infinite reductions (non- termination). Regarded as a model of computation, infinite reductions are unwanted whence their static detection is important. There are string rewriting systems which admit infinite reductions although they admit no loops. Their non-termination is particularly difficult to uncover. We present a few necessary conditions for the existence of loops, and thus establish a means...

Normal cryptogroups with an associate subgroup

Mario Petrich (2013)

Czechoslovak Mathematical Journal

Let S be a semigroup. For a , x ∈ S such that a = a x a , we say that x is an associate of a . A subgroup G of S which contains exactly one associate of each element of S is called an associate subgroup of S . It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup S is a completely regular semigroup whose ℋ -relation is a congruence and S / ℋ is a normal band. Using the representation of S as a strong semilattice of Rees matrix semigroups,...

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