diff --git a/test/SmashProductLie-test.jl b/test/SmashProductLie-test.jl
index ecfc6ae..28cb423 100644
--- a/test/SmashProductLie-test.jl
+++ b/test/SmashProductLie-test.jl
@@ -1,5 +1,5 @@
 @testset "SmashProductLie.jl tests" begin
-    @testset "smash_product; R = $R" for R in [QQ, polynomial_ring(QQ, ["x", "y", "z"])[1]]
+    @testset "smash_product; R = $R" for R in [QQ, cyclotomic_field(4)[1]]
         @testset "sl_2(QQ) ⋉ V" begin
             L = special_linear_lie_algebra(QQ, 2)
             V = standard_module(L)
diff --git a/test/SmashProductLieDeform-test.jl b/test/SmashProductLieDeform-test.jl
index 598991d..f51e842 100644
--- a/test/SmashProductLieDeform-test.jl
+++ b/test/SmashProductLieDeform-test.jl
@@ -1,7 +1,7 @@
 @testset "SmashProductLieDeform.jl tests" begin
 
     @testset "SmashProductLieDeform constructor" begin
-        @testset "R = $R" for R in [QQ, polynomial_ring(QQ, ["x", "y", "z"])[1]]
+        @testset "R = $R" for R in [QQ, cyclotomic_field(4)[1]]
             L = special_orthogonal_lie_algebra(R, 4)
             V = exterior_power(standard_module(L), 2)
             sp = smash_product(L, V)
@@ -55,7 +55,7 @@
     end
 
     @testset "symmetric_deformation constructor" begin
-        @testset "R = $R" for R in [QQ, polynomial_ring(QQ, ["x", "y", "z"])[1]]
+        @testset "R = $R" for R in [QQ, cyclotomic_field(4)[1]]
 
             for (sp, dimL, dimV) in [begin
                 L = special_orthogonal_lie_algebra(R, 4)
@@ -98,7 +98,7 @@
     end
 
     @testset "SmashProductLieDeform sanitize checks" begin
-        @testset "R = $R" for R in [QQ, polynomial_ring(QQ, ["x", "y", "z"])[1]]
+        @testset "R = $R" for R in [QQ, cyclotomic_field(4)[1]]
 
             L = special_orthogonal_lie_algebra(R, 4)
             V = exterior_power(standard_module(L), 2)