A semigroup is a set of elements to which is related an operation usually called multiplication and an equivalence relation, such that the set is closed and associative relative to the operation. We shall discuss, briefly, finite semigroups which are uniquely factorable in the same sense as the multiplicative semigroup of all nonzero integers. Clifford' defined an arithmetic in such a way as to...

Let 5 be a commutative semigroup. For a, b £5, we say that a divides b (or b is a multiple of a), and write a\b, if either a = b or ax = b for some x£5. We say that a properly divides b if a\b and b does not divide a. We call 5 archimedean if for all a, b £5, a divides some power of b. It is known that every commutative semigroup is uniquely expressible as a semilattice of archimedean semigroup...

This paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan &Gilman. A fundamental investigation reveals that the natural definition of a ‘word-hyperbolic structure’ has to be strengthened slightly in order to define a unique semigroup up to isomorphism. The isomorphism problem is proven to be undecidable for word-hyperbolic semigroups (in contrast to the...

In this paper, we study an approximate biflatness of l 1 S , where id="M2"> is a Clifford semigroup. Indeed, show that semigroup algebra id="M3"> approximately biflat if and only every maximal subgroup id="M4"> amenable...

It is known that a left C-wrpp semigroup can be described as curler structure of a left band and a C-wrpp semigroup. In this paper, we introduce the class of weakly left C-wrpp semigroups which includes the class of weakly left C-rpp semigroups as a subclass. We shall particularly show that the spined product of a left C-wrpp semigroup and a right normal band is a weakly left C-wrpp semifroup. ...

decomposability of an algebraic structure into the :union: of its sub-structures goes back to g. scorza's theorem of 1926 for groups. an analogue of this theorem for rings has been recently studied by a. lucchini in 2012. on the study of this problem for non-group semigroups, the first attempt is due to clifford's work of 1961 for the regular semigroups. since then, n.p. mukherjee in ...

1. In a recent paper [4], Sevrin has given necessary and sufficient conditions for a subsemigroup of the free product of a free group and a free semigroup to be of the same form; in particular he deduces that a subsemigroup T oí a free semigroup 5 is free if and only if1 1. For any aET, sES, if as ET and saET, then sET. Now whereas the property of being a free subsemigroup of S is absolute, i.e...

0. Introduction. The literature on algebraic semigroups contains publications concerning two distinct types of semigroup extensions. Ideal extensions of semigroups were introduced by Clifford in [1] whereas Rédei [9] introduced Schreier extensions of monoids (a monoid is a semigroup containing an identity element). Let A and 5 be two disjoint semigroups and let 5" contain a zero element o. A se...

, 773 (2006); 314 Science et al. Clifford B. Saper, Body Temperature BIOMEDICINE: Enhanced: Life, the Universe, and www.sciencemag.org (this information is current as of February 7, 2007 ): The following resources related to this article are available online at http://www.sciencemag.org/cgi/content/full/314/5800/773 version of this article at: including high-resolution figures, can be found in ...

This paper deals with generators A of strongly continuous right linear semigroups in Banach two-sided spaces whose set scalars is an arbitrary Clifford algebra Cℓ(0,n). We study the invertibility operators form P(A), where P(x)∈R[x] any real polynomial, and we give integral representation for P(A)−1 by means a Laplace-type transform semigroup T(t) generated A. In particular, deduce new spherica...