On semigroups admitting ring structure

Peinado, Rolando E.

doi:10.1007/bf02573037

Cited by 13 publications

(4 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we study those rings in which every subsemigroup is a subring, and those in which every semigroup endomorphism is a ring endomorphism. We note in passing that recent work on a rather different, but nonetheless related, question: to characterise certain types of semigroups admitting a ring structure, is to be found in Peinado (1970), Satyanarayana (1971) and Satyanarayana (1973).…”

Section: Introductionmentioning

confidence: 97%

Semigroups in rings

Cresp

Sullivan

1975

J. Aust. Math. Soc.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 97%

Semigroups in rings

Cresp

Sullivan

1975

J. Aust. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Such semigroups are well studied in the literature. We refer the reader to [1][2][3] and [5] for sampling of what is known on ring semigroups. In particular, it is well known that every cyclic ring semigroup (with 1 = 0) is isomorphic to the multiplicative semigroup of a finite field, i.e., to a multiplicative semigroup of the form F p n , where p is a prime number and n is a positive integer (e.g.…”

Section: Theorem 22 Let S Be a Finite Commutative Semigroup Then S mentioning

confidence: 99%

Semigroups whose endomorphisms are power functions

Mazurek

2013

Semigroup Forum

View full text Add to dashboard Cite

For any commutative semigroup S and any positive integer m, the power function f : S → S defined by f (x) = x m is an endomorphism of S. In this paper we characterize finite cyclic semigroups as those finite commutative semigroups whose endomorphisms are power functions. We also prove that if S is a finite commutative semigroup with 1 = 0, then every endomorphism of S preserving 1 and 0 is equal to a power function if and only if either S is a finite cyclic group with zero adjoined or S is a cyclic nilsemigroup with identity adjoined. Immediate consequences of the results are, on the one hand, a characterization of commutative rings whose multiplicative endomorphisms are power functions given by Greg Oman in the paper (Semigroup Forum, 86 (2013), 272-278), and on the other hand, a partial solution of Problem 1 posed by Oman in the same paper.

show abstract

“…We can see from Lawson's theorem that the multiplicative interval semigroup [0, 1] does not admit a ring structure 1 . Consider the multiplicative interval semigroup [a, 1] 1 do not admit a ring structure.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Kemprasit¹,

Danpattanamongkon²,

Savettaseranee³

2010

ScienceAsia

View full text Add to dashboard Cite

ABSTRACT:Lawson has given a sufficient condition for a semigroup S which guarantees that S does not admit a ring structure. From Lawson's theorem, we have that the multiplicative interval semigroup [0, 1] does not admit a ring structure. In this paper we give an elementary proof of this fact. We then show that the multiplicative interval semigroup [a, 1] with −1 a < 0 < a 2 1 does not admit the structure of a ring, a fact which cannot be derived from Lawson's theorem. These facts are then applied to show that every nontrivial multiplicative bounded interval semigroup on R does not admit a ring structure.

show abstract

On semigroups admitting ring structure

Cited by 13 publications

References 35 publications

Semigroups in rings

Semigroups in rings

Semigroups whose endomorphisms are power functions

Untitled

Contact Info

Product

Resources

About