Extending congruences on semigroups

Author:
A. R. Stralka

Journal:
Trans. Amer. Math. Soc. **166** (1972), 147-161

MSC:
Primary 22A15

DOI:
https://doi.org/10.1090/S0002-9947-1972-0294557-9

MathSciNet review:
0294557

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The two main results are: (1) Let *S* be a semigroup which satisfies the relation , let *A* be a subsemigroup of Reg *S* which is a band of groups and let be a congruence on *A*. Then can be extended to a congruence on *S*. (2) Let *S* be a compact topological semigroup which satisfies the relation , let *A* be a closed subsemigroup of Reg *S* and let be a closed congruence on *A* such that . Then can be extended to a closed congruence on *S*.

**[1]**L. W. Anderson and R. P. Hunter,*Homomorphisms and dimension*, Math. Ann.**147**(1962), 248-268. MR**26**#4324. MR**0146804 (26:4324)****[2]**-,*On the infinite subsemigroups of certain compact semigroups*(to appear).**[3]**J. T. Borrego,*Adjunction semigroups*, Bull. Austral. Math. Soc.**1**(1969), 47-58. MR**39**#7021. MR**0245715 (39:7021)****[4]**J. H. Carruth and C. E. Clark,*Representations of certain compact semigroups by HLsemigroups*, Trans. Amer. Math. Soc.**149**(1970), 327-337. MR**41**#8563. MR**0263964 (41:8563)****[5]**A. H. Clifford and G. B. Preston,*The algebraic theory of semigroups*. Vols. 1, 2, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R. I., 1961, 1967. MR**24**#A2627; MR**36**#1558.**[6]**G. Gratzer,*Lectures on lattice theory*, Freeman, San Francisco, Calif., 1971. MR**0321817 (48:184)****[7]**J. M. Howie,*Naturally ordered bands*, Glasgow Math. J.**8**(1967), 55-58. MR**34**#5726. MR**0205900 (34:5726)****[8]**N. Kimura and M. Yamada,*Note on idempotent semigroups*. II, Proc. Japan Acad.**34**(1958), 110-112. MR**20**#4603. MR**0098141 (20:4603)****[9]**J. D. Lawson,*Topological semilattices with small semilattices*, J. London Math. Soc. (2)**1**(1969), 719-724. MR**40**#6576. MR**0253301 (40:6516)****[10]**M. Mislove,*Four problems about compact semigroups*, Dissertation, University of Tennessee, Knoxville, Tenn., 1969.**[11]**K. Numakura,*Theorems on compact totally disconnected semigroups and lattices*, Proc. Amer. Math. Soc.**8**(1957), 623-626. MR**19**, 290. MR**0087032 (19:290d)****[12]**A. R. Stralka,*The Green equivalences and dimension in compact semigroups*, Math. Z.**109**(1969), 169-176. MR**39**#2903. MR**0241563 (39:2903)****[13]**-,*The congruence extension property for compact topological lattices*, Pacific J. Math. (to appear). MR**0304259 (46:3394)****[14]**M. Yamada,*Regular semigroups whose idempotents satisfy permutation identities*, Pacific J. Math.**21**(1967), 371-392. MR**37**#2887. MR**0227302 (37:2887)****[15]**-,*On a regular semigroup in which the idempotents form a band*, Pacific J. Math.**33**(1970), 261-272. MR**0276391 (43:2138)****[16]**A. D. Wallace,*Project MOB*, Lecture Notes, University of Florida, Tallahassee, Fla., 1964, unpublished.

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
22A15

Retrieve articles in all journals with MSC: 22A15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0294557-9

Keywords:
Topological semigroup,
semigroup,
congruence,
naturally ordered band,
*N*-inversive

Article copyright:
© Copyright 1972
American Mathematical Society