id: 03939594
dt: j
an: 03939594
au: Hách, Trâ\=n Lâm
ti: Characterizations of monoids by regular acts.
so: Period. Math. Hung. 16, 273-279 (1985).
py: 1985
pu: Akadémiai Kiadó, Budapest; Springer, Dordrecht
la: EN
cc: 
ut: von Neumann regular; projective acts; S-act; cancellative monoids; regular
    acts; strongly faithful acts
ci: 
li: doi:10.1007/BF01848077
ab: The concept of a regular act is introduced transfering the concept of a
    regular module. The right S-act A is regular if for every $a\in A$
    there exists $f\in Hom\sb S(aS,S)$ such that $af(a)=a$. A monoid which
    is von Neumann regular is a regular act over itself but not conversely.
    There exist monoids over which no act is regular. Exactly for groups
    regular and projective acts coincide but in general neither of the two
    implies the other. Every S-act is regular iff $S=\{0,1\}$ or S is a
    group of prime order, for $\vert S\vert >1$. Left cancellative monoids
    S are characterized as regular acts over which regular acts and
    strongly faithful acts coincide. The S-act A is called strongly
    faithful if $as=at$ implies $s=t$ for $a\in A$, s,t$\in S$.
rv: U.Knauer