On lattice-ordered rings in which the square of every element is positive

Steinberg, Stuart A.

doi:10.1017/s1446788700014804

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1980

2021

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Cited by 23 publications

(6 citation statements)

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“…The characterization (vi) for unital 1-algebras goes back to S. A. Steinberg [33]. Condition (vii) turns out to be very important in I-algebra theory.…”

Section: Huijsmansmentioning

confidence: 96%

Lattice-Ordered Algebras and f-Algebras: A Survey

Huijsmans

1991

Studies in Economic Theory

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“…The characterization (vi) for unital 1-algebras goes back to S. A. Steinberg [33]. Condition (vii) turns out to be very important in I-algebra theory.…”

Section: Huijsmansmentioning

confidence: 96%

Lattice-Ordered Algebras and f-Algebras: A Survey

Huijsmans

1991

Studies in Economic Theory

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“…(c) implies (b). By Steinberg (1976), Lemma 5, the idempotents of S are central, and since the idempotents of S = S/J(S) can be lifted to S, the regular ring S is strongly regular by Lambek (1966), p. 102. Since J(S) is convex, S is a po-ring.…”

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confidence: 98%

Lattice-ordered modules of quotients

Steinberg

1980

J Aust Math Soc A

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Let Q be the ring of quotients of the/-ring R with respect to a positive hereditary torsion theory and suppose Q is a right/-ring. It is shown that if the finitely-generated right ideals of R are principal, then Q is an/-ring. Also, if Q R is injective, Q is an/ring if and only if its Jacobson radical is convex. Moreover, a class of po-rings is introduced (which includes the classes of commutative po-rings and right convex/-rings) over which Q(M) is an /-module for each/-module M.

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“…Thus R = ¿U (T© rx) by Lemma 1. In [6,Remark,p. 367] Steinberg defined an /-ring R to be supertessimal if n\x\ < \x2\ for each n e Z+ and x e R. Theorem 3.…”

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confidence: 99%