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Do we have to write setter method to use #Inject annotation?

is it mandatory to write a setter function when we use #Inject annotation

Nope. It is not mandatory. Reflection is used to set the value.
See this and this for more info.

No, we don,t have to write the setter method for #Inject, it is same annotation as the #Autowired.
#Inject is part of a Java technology called CDI that defines a standard for dependency injection similar to Spring. In a Spring application, the two annotations works the same way as Spring has decided to support some JSR-299 annotations in addition to their own.
#Inject can be injected the reference to the implementation of the Provider interface, which allows injecting the deferred references.

Saving entities in private methods

I have an Ingestion class that exposes a single method ingest. This method processes each section of a passed in form (section 1, section 2, etc, etc).
I have private methods for each section, saving the entity as it processes through. I'm aware that #Transactional has no effect on private methods, however I do not want to expose these methods but would like to use the functionality that #Transactional provides.
I'm looking to make sure each section completes in its own Transaction; I could do this through 'AspectJ' (as other SO answers have suggested) instead of Spring's out the box implementation, but I am trying to avoid due to the system wide changes it would cause.
Any thoughts on another approach?
The pseudo code provided below gives a general idea on the structure of the class:
public Class Ingestion {
// Autowired Repo's
...
...
#Transactional
public void ingest(Form form){
this.processSection1(form);
this.processSection2(form);
this.processSection3(form);
}
#Transactional
private void processSection1(Form form){
// do specific section 1 logic
section1Repo.save(form);
}
#Transactional
private void processSection2(Form form){
// do specific section2 logic
section2Repo.save(form);
}
#Transactional
private void processSection3(Form form){
// do specific section3 logic
section3Repo.save(form);
}
}
=========================================================================
This is not a duplicate question as marked in the comments. I know #Transactional doesnt work on private methods. My question is more along the lines of 'how do we get around this Spring AOP issue without having to use AspectJ'

The reason this doesn't work is that annotations like #Transactional add additional functionality that is intercepted by Spring's proxy object that wraps the actual object. But when you call a private method on an object with the this keyword, you're going straight to the real object and bypassing the proxy.
One way to solve this is to #Autowire the object into itself, and make the transactional calls via that autowired variable. You can still access private methods that way, and the call will be to a Spring-managed proxy instead of the bare object.

You may extract these three processing methods in another class, make them public, but set the class constructor access level to package-local (but not private, since Spring can't proxy classes with private constructors), so no classes from other packages could access these methods just because they are not able to instantiate their class. It doesn't hide these methods completely, but may fit your needs. This trick can be done with an inner class as well (note that it must be declared with package-local access).
To completely hide these methods, you may make use of declarative transaction management by injecting TransactionTemplate bean and using its execute method in private methods. This feature comes out-of-the-box. See more here.
Also, take note that for creating new transaction on executing method B from method A, method B must be declared #Transactional with propagation type REQUIRES_NEW. Otherwise, any nested methods will be invoked in the same transaction started by initial calling method.

Will an annotation on the interface persist on the implementation?

I have this technical doubt...
If I have an interface
public interface test{
#Transactional
public void mymethod();
}
and then I have my implementation
public class testImpl implements test{
#Override
public void mymethod(){
//..do something
}
}
Since I am using #Override, will my annotation #Transactional, #Lock or any other persist on my implementation? or will overriden by the interface method without adding any special behaviour from the annotation?

Best answer I have read on this matter:
See this link https://stackoverflow.com/a/5551597/3447634
COPY OF THAT ANSWER:
"It really all depends on your application architecture, in my opinion. It depends on how you are proxying your classes. If you have your app set to "proxy-target-class='true'" (in your application context, then your #Transactional information wont be picked up if you annotate the Interface.
Check out The Spring Docs -- "Tips" for more information.
Spring recommends that you only annotate concrete classes (and methods of concrete classes) with the #Transactional annotation, as opposed to annotating interfaces. You certainly can place the #Transactional annotation on an interface (or an interface method), but this works only as you would expect it to if you are using interface-based proxies. The fact that Java annotations are not inherited from interfaces means that if you are using class-based proxies (proxy-target-class="true") or the weaving-based aspect (mode="aspectj"), then the transaction settings are not recognized by the proxying and weaving infrastructure, and the object will not be wrapped in a transactional proxy, which would be decidedly bad."

Spring recommendations: proxying mechanism vs #Transactional on class or interface

Spring doc has the two recommendations:
Spring recommends that you only annotate concrete classes (and methods
of concrete classes) with the #Transactional annotation, as opposed to
annotating interfaces. You certainly can place the #Transactional
annotation on an interface (or an interface method), but this works
only as you would expect it to if you are using interface-based
proxies. The fact that Java annotations are not inherited from
interfaces means that if you are using class-based proxies
(proxy-target-class="true") or the weaving-based aspect
(mode="aspectj"), then the transaction settings are not recognized by
the proxying and weaving infrastructure, and the object will not be
wrapped in a transactional proxy, which would be decidedly bad.
(from http://static.springsource.org/spring/docs/3.0.x/reference/transaction.html)
and
Spring AOP uses either JDK dynamic proxies or CGLIB to create the
proxy for a given target object. (JDK dynamic proxies are preferred
whenever you have a choice).
(from http://static.springsource.org/spring/docs/3.0.x/reference/aop.html#aop-understanding-aop-proxies)
Do I understand correctly that in order to follow both recommendations, I need to have #Transactional annotation on concrete class, but still provide an interfaces (that this class implements) containing all transactional methods, so that Spring can use JDK dynamix proxies for this interface?

It works like this
Have a business interface with methods, do not annotate interface methods with #Transactional
Write an implementation class for interface defined above and annotate methods in impl class with #Transactional
As spring recommends usage of JDK dynamic proxies which are interface based hence we need to have business interface in place.
Also, as stated
Java annotations are not inherited from interfaces
We need to annotate concrete / implementation class methods with #Transactional

Where should I put #Transactional annotation: at an interface definition or at an implementing class?

The question from the title in code:
#Transactional (readonly = true)
public interface FooService {
void doSmth ();
}
public class FooServiceImpl implements FooService {
...
}
vs
public interface FooService {
void doSmth ();
}
#Transactional (readonly = true)
public class FooServiceImpl implements FooService {
...
}

From http://static.springsource.org/spring/docs/2.0.x/reference/transaction.html
The Spring team's recommendation is that you only annotate concrete classes with the #Transactional annotation, as opposed to annotating interfaces. You certainly can place the #Transactional annotation on an interface (or an interface method), but this will only work as you would expect it to if you are using interface-based proxies. The fact that annotations are not inherited means that if you are using class-based proxies then the transaction settings will not be recognised by the class-based proxying infrastructure and the object will not be wrapped in a transactional proxy (which would be decidedly bad). So please do take the Spring team's advice and only annotate concrete classes (and the methods of concrete classes) with the #Transactional annotation.
Note: Since this mechanism is based on proxies, only 'external' method calls coming in through the proxy will be intercepted. This means that 'self-invocation', i.e. a method within the target object calling some other method of the target object, won't lead to an actual transaction at runtime even if the invoked method is marked with #Transactional!
(Emphasis added to the first sentence, other emphasis from the original.)

Spring's recommendation is that you annotate the concrete implementations instead of an interface. It's not incorrect to use the annotation on an interface, it's just possible to misuse that feature and inadvertently bypass your #Transaction declaration.
If you've marked something transactional in an interface and then refer to one of its implementing classes elsewhere in spring, it's not quite obvious that the object that spring creates will not respect the #Transactional annotation.
In practice it looks something like this:
public class MyClass implements MyInterface {
private int x;
public void doSomethingNonTx() {}
#Transactional
public void toSomethingTx() {}
}

You can put them on the interface but be warn that transactions may not end up happening in some cases. See the second tip in Secion 10.5.6 of the Spring docs:
Spring recommends that you only annotate concrete classes (and methods of concrete classes) with the #Transactional annotation, as opposed to annotating interfaces. You certainly can place the #Transactional annotation on an interface (or an interface method), but this works only as you would expect it to if you are using interface-based proxies. The fact that Java annotations are not inherited from interfaces means that if you are using class-based proxies (proxy-target-class="true") or the weaving-based aspect (mode="aspectj"), then the transaction settings are not recognized by the proxying and weaving infrastructure, and the object will not be wrapped in a transactional proxy, which would be decidedly bad.
I would recommend putting them on the implementation for this reason.
Also, to me, transactions seem like an implementation detail so they should be in the implementation class. Imagine having wrapper implementations for logging or test implementations (mocks) that don't need to be transactional.

Supporting #Transactional on the concrete classes:
I prefer to architect a solution in 3 sections generally: an API, an Implementation and a Web (if needed). I try my best to keep the API as light/simple/POJO as possible by minimizing dependencies. It's especially important if you play it in a distributed/integrated environment where you have to share the APIs a lot.
Putting #Transactional requires Spring libraries in the API section, which IMHO is not effective. So I prefer to add it in the Implementation where the transaction is running.

Putting it on the interface is fine as long all foreseeable implementers of your IFC care about TX data (transactions aren't problems that just databases deal with). If the method doesn't care about TX (but you need to put it there for Hibernate or whatever), put it on the impl.
Also, it might be a bit better to place #Transactional on the methods in the interface:
public interface FooService {
#Transactional(readOnly = true)
void doSmth();
}