Fausset's Bible Dictionary 
1. The Hittite Elon's daughter; wife of Esau ( Genesis 26:34). Called Adah in the genealogy of Edom ( Genesis 36:2-3). (See Adah .) Bashemath is doubtless a name of praise conferred on her at marriage.
2. Ishmael's daughter; the last of Esau's three wives according to the Edomite genealogy inserted by Moses ( Genesis 36:3-4; Genesis 36:13). From her son Reuel four Edomite tribes descended. Called Mahalath in the narrative, Genesis 28:9. Esau's Seirite wife, called Judith daughter of Beeri in the narrative ( Genesis 26:34), is called Arolibamah (the name of a district in Idumaea) the genealogy ( Genesis 36:41). (See AROLIBAMAH.)
3. Solomon's daughter, married to Ahimaaz, one of his commissariat officers ( 1 Kings 4:15).
Morrish Bible Dictionary 
One of the wives of Esau, the daughter of Ishmael and the mother of Reuel. Genesis 36:3,4 . In the earlier narrative, Genesis 26:34; Genesis 28:9 , the names of Esau's wives differ from those given in Genesis 36:2,3 . The women may have had two names, or another name have been given them on their marriage. It appears probable that Bashemath, daughter of Elon, is the same as ADAH, daughter of Elon; and that Bashemath, daughter of Ishmael, is the same as MAHALATH, daughter of Ishmael. JUDITH, daughter of Beeri, may be the same as Aholibamah daughter of Anah, if Beeri is her father's name and Anah her mother's.
Easton's Bible Dictionary 
Bibliography Information Easton, Matthew George. Entry for 'Bashemath'. Easton's Bible Dictionary. https://www.studylight.org/dictionaries/eng/ebd/b/bashemath.html. 1897.
Smith's Bible Dictionary 
Bash'emath. (Fragrant, Pleasing). Daughter of Ishmael, the last married of the three wives of Esau. Genesis 26:34; Genesis 36:3-4; Genesis 36:13. (B.C. after 1797). In Genesis 28:9, she is called Mahalath .
Holman Bible Dictionary 
Cyclopedia of Biblical, Theological and Ecclesiastical Literature 
(Heb. Basmath', בִּשְׂמִת , elsewhere more correctly Anglicized "Basmath," q.v.), the name of two females.
1. A daughter of Ishmael, the last married (B.C. 1926) of the three wives of Esau ( Genesis 36:3-4; Genesis 36:13), from whose son, Reuel, four tribes of the Edomites were descended. When first mentioned she is called Mahalath ( Genesis 28:9); while, on the other hand, the name Bashemath is in the narrative ( Genesis 26:34) given to another of Esau's wives, the daughter of Elon the Hittite. It is remarkable that all Esau's wives receive different names in the genealogical table of the Edomites (Genesis 36) from those by which they have been previously mentioned in the history. Thus:
( Genesis 36:2-3.) ( Genesis 26:34; Genesis 28:9 )
1. Adah, daughter of Elon. 2. Bashemath, d. of Elon.
2. Aholibamah, d. of Anah. 1. Judith, d. of Beeri.
3. Bashemath, d. of Ishmael. 3. Mahalath, d. of Ishmael.
Whatever be the explanation of this diversity of names, there is every reason for supposing that they refer to the same persons respectively, and we may well conclude with Hengstenberg that the change of all the names cannot have arisen from accident; and, farther, that the names in the genealogical table, which is essentially an Edomitish document, are those which these women respectively bore as the wives of Esau (Hengstenberg, Auth. d. Pent. 2:277; English transl. 2:226). This view is confirmed by the fact that the Seirite wife, who is called Judith in the narrative, appears in the genealogical account under the name of Aholibamah (q.v.), a name which appears to have belonged to a district of Idumaea ( Genesis 36:41). The only ground for hesitation or suspicion of error in the text is the occurrence of this name Bashemath both in the narrative and the genealogy, though applied to different persons. The Samaritan text seeks to remove this difficulty by reading Mahalath instead of Bashemath in the genealogy. We might with more probability suppose that this name (Bashemath) has been assigned to the wrong person in one or other of the passages; but if so, it is impossible to determine which is erroneous. (See Esau).