this is mostly called "ijaza(h)" - without or without the h - a certificate that is globally valid to be able to teach Islamic religious sciences. Of course you'd need to provide some kind of explanation in a footnote or parenthesis. AFAIK, although there is "imam training" available in the US and Europe, nothing is available that comes close to the above qualification so there is no "equivalent degree".
For help with a definition, please see the following:
http://en.wikipedia.org/wiki/Ijazah
http://www.ibnjabal.com/teacher.html
At Al-Azhar, he received ijazah from Shaikh Mustafa Ismail

The phrase used is "to obtain ijaza(h) at/from...."

على حد علمي واستناداً إلى بعض المراجع التي استعنت بها، اعتادت جامعة الأزهر منح الدرجات الآتية
العالمية : تعني الدرجة الجامعية الأولى وهي الليسانس = BA
وهي درجة تمتد لأربع سنوات دراسية، وللطالب الحق في اختصارهن عامين إذا تمكن من ذلك

ويليها درجة التخصص أو الدراسات العليا، ويطلق عليها
إجازة العالمية وأيضاً يطلق عليها العالمية بإجازة، و شهادة التخصص، وتمتد لسنتين اثنتين

ثم درجة الدكتوراه وتسمى
العالمية العليا

Al Alamiya (was absent in all versions of translations) It is either the name of the college or as it meant global. Second nobody said it is a BA it is a certificate, it is not even a diploma

“In 1294 (Higri), 1877 A.D., Muhammad Abdu applied for Al Alamia Exam, but being well known as one of Al Afghany’s students, he was considered an fundamentalist. From Al Azhar's inflexible scholars' point of view, being in contact with Al Afghany, was like committing a sin.



They took upon themselves failing him by asking him questions that they thought were insuperable. Competently, though, he answered the questions set. Sheikh Mahdy Abaasy- Chief of committee and Head of Al- azhar at the time, swore that had he known a better status than first place, he would have granted it to Muhammad Abdu. Eventually, to avoid disputes among committee members, Sheikh Muhammad Abdu was granted the certificate of Al Alamia of the second degree, at the age of 28.





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Note added at 4 hrs (2007-09-11 18:57:21 GMT)
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From amongst his most famous teachers was the highly respected Azhari hadith specialist Shaikh Muhammad Zaki Ibrahim, a colleauge of the late grand Shaikh of al-Azhar Abdul Halim Mahmud, and one of the last of those who possessed the lofty al-‘alamia al-qadim certificate of al-Azhar.

http://www.themodernreligion.com/profile/sh-Al-Sayyid-Ibrahi...

An educated guess. Note I believe here عالمية implies Scholars' or Scholarly

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Note added at 3 hrs (2007-09-11 17:05:11 GMT)
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Adding to my response to Profi..., studies is used as in the same context as social studies. One is not exactly certain if this is not menat to be a degree or otherwise, because the Asker, as Fuad has rightfully said, did not provide sufficient context to even suggest that this is only issued by a "traditional" institute.

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Note added at 3 hrs (2007-09-11 17:10:22 GMT)
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To reinforce the propriety of the use of studies in even a modern institutional context, see this link:
http://www.islamic-college.co.ae/

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Note added at 6 hrs (2007-09-11 20:48:20 GMT)
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I have found the exact translation:

Certificates provided by the faculty
The Bechelor degree
The Masters degree
The PhD


الدرجات العلمية التى تمنحها الكلية عدد أعضاء هيئة التدريس: 88
عدد أعضاء هيئة التدريس المعاونة: 46

1- الإجازة العالية ( البكالوريوس )
2- درجة التخصص ( الماجستير )
3- درجة العالمية ( الدكتوراه )

See this link for table showing certificates given by Al-Azhar Faculty of Islamic and Arabic Studies for Girls in Alexanderia and look under Cetificates given:
http://www.azhar.edu.eg/Azhar/fac_pages/eslamya_alex_banat.h...

The answer then is PhD Degree (or certificates as translated in the web site) in Arabic and Islamic Studies.

Note the same translation appears in all the Faculties of Azhar which gave this degree/certificate

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Note added at 6 hrs (2007-09-11 20:51:20 GMT)
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Again the appropriate translation is:

PhD. DEGREE (OR CERTIFICATES AS TRANSLATED IN THE WEB SITE) IN ARABIC AND ISLAMIC STUDIES

I have found the exact translation:

Certificates provided by the faculty
The Bechelor degree
The Masters degree
The PhD


الدرجات العلمية التى تمنحها الكلية عدد أعضاء هيئة التدريس: 88
عدد أعضاء هيئة التدريس المعاونة: 46

1- الإجازة العالية ( البكالوريوس )
2- درجة التخصص ( الماجستير )
3- درجة العالمية ( الدكتوراه )

See this link for table showing certificates given by Al-Azhar Faculty of Islamic and Arabic Studies for Girls in Alexanderia and look under Cetificates given:
http://www.azhar.edu.eg/Azhar/fac_pages/eslamya_alex_banat.h...

The answer then is PhD Degree (or certificates as translated in the web site) in Arabic and Islamic Studies.

Note the same translation appears in all the Faculties of Azhar which gave this degree/certificate

International Certification in Arabic and Islamic Sciences (ICAIS)

Irrespective of its equivalents, this is the exact meaning of the word. Scholars are "ulema", plular of "alem" (scholar).

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Note added at 1 day23 hrs (2007-09-13 13:29:03 GMT)
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"At El Azhar University the degree gained after passing the exam is the very famous Alamia, or a learned scholar, a docent."
(http://sexualeconomy.net/a/iraq/classstruggle.pdf)

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Note added at 1 day23 hrs (2007-09-13 13:30:33 GMT)
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"Now, the type of Alamia or degree of learned scholar given to a foreign student was known among the inner circles of Al Azhar as Alamiat Aghraab, foreign student degree. "
(ibid)

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Note added at 1 day23 hrs (2007-09-13 13:34:41 GMT)
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So, it means scholarship, or degree of degree of learned scholar, and since it's culture-specific, we should transliterate it as "Alamia" or "Alamiyya". No one seems to write it "alem" with e instead of (to represent the kasra diacrtic), a common mistake.