The unitability of -prime lattice-ordered rings with squares positive

Author:
Jing Jing Ma

Journal:
Proc. Amer. Math. Soc. **121** (1994), 991-997

MSC:
Primary 06F25; Secondary 16W80

DOI:
https://doi.org/10.1090/S0002-9939-1994-1186988-X

MathSciNet review:
1186988

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that an *l*-prime lattice-ordered ring with squares positive and an *f*-superunit can be embedded in a unital *l*-prime lattice-ordered ring with squares positive.

**[1]**S. A. Steinberg,*On the unitability of a class of partially ordered rings that have squares positive*, J. Algebra**100**(1986), 325-343. MR**840580 (88b:16070)****[2]**-,*Unital l-prime lattice-ordered rings with polynomial constraints are domains*, Trans. Amer. Math. Soc.**276**(1983), 145-164. MR**684499 (84d:16050)****[3]**D. G. Johnson,*A structure theory for a class of lattice-ordered rings*, Acta. Math.**104**(1960), 163-215. MR**0125141 (23:A2447)****[4]**P. Conrad,*Some structure theorems for lattice-ordered groups*, Trans. Amer. Math. Soc.**99**(1961), 212-240. MR**0121405 (22:12143)****[5]**Ma Jingjing,*On lattice-ordered rings with polynomial constraints*, J. Math. Res. Exposition**11**(1991), 325-330. (Chinese) MR**1123387 (92g:16060)****[6]**S. A. Steinberg,*On lattice-ordered rings in which the square of every element is positive*, J. Austral. Math. Soc.**22**(1976), 362-370. MR**0427198 (55:233)****[7]**M. Henriksen and J. Isbell,*Lattice-ordered rings and function rings*, Pacific J. Math.**12**(1962), 533-565. MR**0153709 (27:3670)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
06F25,
16W80

Retrieve articles in all journals with MSC: 06F25, 16W80

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1186988-X

Keywords:
Lattice-ordered ring,
*l*-prime *l*-ring,
unitability,
squares positive

Article copyright:
© Copyright 1994
American Mathematical Society