diff --git a/modin/pandas/base.py b/modin/pandas/base.py
index f3992d0db6d..282d27eaf67 100644
--- a/modin/pandas/base.py
+++ b/modin/pandas/base.py
@@ -1868,8 +1868,6 @@ def idxmax(self, axis=0, skipna=True, numeric_only=False):  # noqa: PR01, RT01,
         """
         Return index of first occurrence of maximum over requested axis.
         """
-        if not all(d != pandas.api.types.pandas_dtype("O") for d in self._get_dtypes()):
-            raise TypeError("reduce operation 'argmax' not allowed for this dtype")
         axis = self._get_axis_number(axis)
         return self._reduce_dimension(
             self._query_compiler.idxmax(
@@ -1881,8 +1879,6 @@ def idxmin(self, axis=0, skipna=True, numeric_only=False):  # noqa: PR01, RT01,
         """
         Return index of first occurrence of minimum over requested axis.
         """
-        if not all(d != pandas.api.types.pandas_dtype("O") for d in self._get_dtypes()):
-            raise TypeError("reduce operation 'argmin' not allowed for this dtype")
         axis = self._get_axis_number(axis)
         return self._reduce_dimension(
             self._query_compiler.idxmin(
diff --git a/modin/pandas/dataframe.py b/modin/pandas/dataframe.py
index f07ec94b18c..adc46bdf210 100644
--- a/modin/pandas/dataframe.py
+++ b/modin/pandas/dataframe.py
@@ -620,7 +620,7 @@ def transpose(self, copy=False, *args) -> DataFrame:  # noqa: PR01, RT01, D200
             query_compiler=self._query_compiler.transpose(*args)
         )
 
-    T = property(transpose)
+    T: DataFrame = property(transpose)
 
     def add(
         self, other, axis="columns", level=None, fill_value=None
diff --git a/modin/pandas/series.py b/modin/pandas/series.py
index b3cfc065e2c..91f1a945bed 100644
--- a/modin/pandas/series.py
+++ b/modin/pandas/series.py
@@ -2088,7 +2088,7 @@ def transpose(self, *args, **kwargs) -> Series:  # noqa: PR01, RT01, D200
         """
         return self
 
-    T = property(transpose)
+    T: Series = property(transpose)
 
     def truediv(
         self, other, level=None, fill_value=None, axis=0
diff --git a/modin/tests/pandas/dataframe/test_reduce.py b/modin/tests/pandas/dataframe/test_reduce.py
index 8f78b4761d5..eba5b9341af 100644
--- a/modin/tests/pandas/dataframe/test_reduce.py
+++ b/modin/tests/pandas/dataframe/test_reduce.py
@@ -220,6 +220,14 @@ def test_idxmin_idxmax(data, axis, skipna, is_transposed, method):
     )
 
 
+@pytest.mark.parametrize("axis", [0, 1])
+def test_idxmin_idxmax_string_columns(axis):
+    # https://github.com/modin-project/modin/issues/7093
+    modin_df, pandas_df = create_test_dfs([["a", "b"]])
+    eval_general(modin_df, pandas_df, lambda df: df.idxmax(axis=axis))
+    eval_general(modin_df, pandas_df, lambda df: df.idxmin(axis=axis))
+
+
 @pytest.mark.parametrize("data", test_data_values, ids=test_data_keys)
 def test_last_valid_index(data):
     modin_df, pandas_df = pd.DataFrame(data), pandas.DataFrame(data)
diff --git a/modin/tests/pandas/utils.py b/modin/tests/pandas/utils.py
index 1f2fa09c54f..f374071cef8 100644
--- a/modin/tests/pandas/utils.py
+++ b/modin/tests/pandas/utils.py
@@ -11,6 +11,8 @@
 # ANY KIND, either express or implied. See the License for the specific language
 # governing permissions and limitations under the License.
 
+from __future__ import annotations
+
 import csv
 import functools
 import itertools
@@ -1084,14 +1086,14 @@ def eval_io_from_str(csv_str: str, unique_filename: str, **kwargs):
     )
 
 
-def create_test_dfs(*args, **kwargs):
+def create_test_dfs(*args, **kwargs) -> tuple[pd.DataFrame, pandas.DataFrame]:
     post_fn = kwargs.pop("post_fn", lambda df: df)
-    return map(
-        post_fn, [pd.DataFrame(*args, **kwargs), pandas.DataFrame(*args, **kwargs)]
+    return tuple(
+        map(post_fn, [pd.DataFrame(*args, **kwargs), pandas.DataFrame(*args, **kwargs)])
     )
 
 
-def create_test_series(vals, sort=False, **kwargs):
+def create_test_series(vals, sort=False, **kwargs) -> tuple[pd.Series, pandas.Series]:
     if isinstance(vals, dict):
         modin_series = pd.Series(vals[next(iter(vals.keys()))], **kwargs)
         pandas_series = pandas.Series(vals[next(iter(vals.keys()))], **kwargs)