Prime and Semiprime Semigroup algebras

of cancellative semigroups

Author:
M. V. Clase

Journal:
Trans. Amer. Math. Soc. **350** (1998), 1991-2007

MSC (1991):
Primary 16S36; Secondary 16N60, 20M25

DOI:
https://doi.org/10.1090/S0002-9947-98-01922-9

MathSciNet review:
1422893

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient conditions are given for a semigroup algebra of a cancellative semigroup to be prime and semiprime. These conditions were proved necessary by Okninski; our contribution is to show that they are also sufficient. The techniques used in the proof are a new variation on the -methods which were developed originally for group algebras.

**1.**J. Bergen and D. S. Passman,*Delta methods in enveloping rings*, J. Algebra**133**(1990), 277-312. MR**92b:16056****2.**-,*Delta methods in enveloping algebras of Lie superalgebras*, Trans. Amer. Math. Soc.**334**(1992), 259-280. MR**93a:17008****3.**-,*Delta methods in enveloping rings II*, J. Algebra**156**(1993), 494-534. MR**94j:16044****4.**-,*Delta methods in enveloping algebras of Lie superalgebras II*, J. Algebra**166**(1994), 568-610. MR**95j:17007****5.**A. H. Clifford and G. B. Preston,*The algebraic theory of semigroups*. Vols. I, II, American Mathematical Society, Providence, Rhode Island, 1961, 1967. MR**24:A2627**; MR**36:1558****6.**I. G. Connell,*On the group ring*, Canad. J. Math.**15**(1963), 650-685. MR**27:3666****7.**J. Krempa,*Special elements in semigroup rings*, Bull. Acad. Polon. Sci. Sér. Sci. Math.**28**(1980), 17-23. MR**82g:20103****8.**J. Okni\'{n}ski,*Semigroup algebras*, Marcel Dekker, New York, 1991. MR**92f:20076****9.**-,*Prime and semiprime semigroup rings of cancellative semigroups*, Glasgow Math. J.**35**(1993), 1-12. MR**93j:16012****10.**D. S. Passman,*Nil ideals in group rings*, Michigan Math. J.**9**(1962), 375-384. MR**26:2470****11.**-,*Radicals of twisted group rings*, Proc. London Math. Soc. (3)**20**(1970), 409-437. MR**42:6129****12.**-,*The algebraic structure of group rings*, John Wiley and Sons, New York, 1977. MR**81d:16001****13.**-,*Semiprime and prime crossed products*, J. Algebra**83**(1983), 158-178. MR**85b:16008****14.**-,*Infinite crossed products and group-graded rings*, Trans. Amer. Math. Soc.**284**(1984), 707-727. MR**85j:16012****15.**-,*Infinite crossed products*, Academic Press, Boston, 1989. MR**90g:16002**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (1991):
16S36,
16N60,
20M25

Retrieve articles in all journals with MSC (1991): 16S36, 16N60, 20M25

Additional Information

**M. V. Clase**

Affiliation:
86 Herkimer St., Apt. A, Hamilton, Ontario, Canada L8P 2G7

Address at time of publication:
Andyne Computing Ltd., 1 Research Drive, Dartmouth, Nova Scotia, B2Y 4M9 Canada

Email:
michael.clase@ns.sympatico.ca

DOI:
https://doi.org/10.1090/S0002-9947-98-01922-9

Received by editor(s):
November 17, 1995

Received by editor(s) in revised form:
August 1, 1996

Additional Notes:
This work was completed while the author held an NSERC Postdoctoral Fellowship at McMaster University, Hamilton, Canada.

Article copyright:
© Copyright 1998
American Mathematical Society