A public opinion survey was carried out in Montana to ascertain if the public identifies a level of benthic (bottom-attached) river and stream algae that is undesirable for recreation. The survey had two parts; an On-River survey and a By-Mail survey. The On-River survey was conducted via 44 trips randomly scheduled throughout the state during which recreators were interviewed in-person at the stream. Selection of stream segments and survey dates ⁄ times was based on known, statewide recreational use patterns. By-Mail survey forms were sent to 2,000 individuals randomly selected from Montana's Centralized Voter File (CVF) available from the Montana Secretary of State. The CVF was current through 2004 and represented over 85% of the state's eligible voting population. In both surveys, eight randomly ordered photographs depicting varying levels of stream benthic algae were presented, and participants were asked if the algae level shown was desirable or undesirable for recreation. Survey form design, selection of photographs, and pretesting followed acceptable protocols that limited unintentional bias through survey execution. There were 433 returned forms (389 complete) for the By-Mail survey, while the On-River survey documented 563 interviews. In both surveys, as benthic algal chlorophyll a (Chl a) levels increased, desirability for recreation decreased. (Other measures of benthic algae biomass are presented as well.) For the public majority, mean benthic Chl a levels ‡200 mg ⁄ m 2 were determined to be undesirable for recreation, whereas mean levels £150 mg Chl a ⁄ m 2 were found to be desirable. Error rates were within the survey's statistical design criteria (£5%). The largest potential error source was nonresponse in the By-Mail survey; however, the population represented by nonrespondents would have to exhibit profoundly different perceptions of river and stream algae to meaningfully alter the results. Results support earlier work in the literature suggesting 150 mg Chl a ⁄ m 2 represents a benthic algae nuisance threshold.(KEY TERMS: rivers ⁄ stream; algae; environmental regulations; environmental impacts; public participation.)Suplee, Michael W

Using an example of Fuchs ll], we can also apply our construction to show that a pseudo-injective module which is not quasi-injective may have arbitrarily large Loewy length.

Abstract. Let it be a property of rings that satisfies the conditions that (i) homomorphic images of w-rings are »r-rings and (ii) ideals of w-rings are w-rings. Let S be a semilattice P of semigroups Sa. If each semigroup ring R[Sa] (a e P) is v-semisimple, then the semigroup ring R[Sa) is also ir-semisimple. Conditions are found on P to insure that each R[Sa] (a G P) is w-semisimple whenever S is a strong semilattice P of semigroups Sa and R{S] is ir-semisimple. Examples are given to show that the conditions on P cannot be removed. These results and examples answer several questions raised by J. Weissglass.Let it be a property of rings. A ring is called a ir-ring if it has property it. An ideal / of a ring is a it-ideal if / is a w-ring. A ring is m-semisimple if it has no nonzero w-ideals. Henceforth, we assume that the property m satisfies the conditions, (i) homomorphic images of w-rings are w-rings and (ii) ideals of w-rings are w-rings. For example, the properties of being nil, nilpotent, or left quasi-regular are such properties.Let A be a ring and let S be a semigroup.

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